139,330 research outputs found
Existence of Multiple Solutions for Quasilinear Systems via Fibering Method
No full textBy using the fibering method introduced by Pohozaev, we prove existence of multiple solutions for a Diriclhlet problem associated to a quasilinear system involving a pair of ðp; qÞ- Laplacian operators
Lie Symmetries and Criticality of Semilinear Differential Systems
No full textWE STUDY LIE SIMMETRIES OF VARIOUS QUASILINEAR OPERATORS AND DERIVE INTEGRAL IDENTITIES. SEVERAL APPLICATIONS ARE PRESENTE
Group Classification Of Semilinear Kohn-laplace Equations
No full textWe study the Lie point symmetries of semilinear Kohn-Laplace equations on the Heisenberg group H1 and obtain a complete group classification of these equations. © 2007 Elsevier Ltd. All rights reserved.68925522568American Mathematical Society, MathSciNet Search, Matches for: Heisenberg group, Number of Matches = 624, 15 January 2007Baaquie, B.E., Yim, K.K., Sigma model Lagrangian for the Heisenberg group (2005) Phys. Lett. B, 615, pp. 134-140Beals, R., Geometry and PDE on the Heisenberg group: A case study (2001) Contemp. Math., 285, pp. 21-27Biagini, S., Positive solutions for a semilinear equation on the Heisenberg group (1995) Boll. Unione. Mat. Ital. Sez. B (7), 9, pp. 883-900Birindelli, I., Capuzzo Dolcetta, I., Cutri, A., Indefinite semi-linear equations on the Heisenberg group: A priori bounds and existence (1995) Comm. Partial Differential Equations, 23, pp. 1123-1157Birindelli, I., Lanconelli, E., A negative answer to a one-dimensional symmetry problem in the Heisenberg group (2003) Calc. Var. Partial Differential Equations, 18, pp. 357-372Bluman, G.W., Simplifying the form of Lie groups admitted by a given differential equation (1990) J. Math. Anal. Appl., 145, pp. 52-62Bluman, G.W., Kumei, S., (1989) Symmetries and Differential Equations, , Springer, New YorkBozhkov, Y., Noether symmetries and critical exponents (2005) SIGMA Symmetry Integrability Geom. Methods Appl., 1. , 12. Paper 022, electronicBozhkov, Y., Divergence symmetries of semilinear polyharmonic equations involving critical nonlinearities (2006) J. Differential Equations, 225, pp. 666-684Y. Bozhkov, I.L. Freire, Divergence symmetries of critical Kohn-Laplace equations on Heisenberg groups, Quaderni Matematici, n. 571, Università di Trieste, 2006, Differ. Equ (Differ. Uravn) (2007) (in press)Y. Bozhkov, I.L. Freire, Conservation laws for critical semilinear Kohn-Laplace equations on the Heisenberg group, 2007, R. P. 04/07, February 2007, IMECC-UNICAMP (submitted for publication)Y. Bozhkov, I.L. Freire, Invariant solutions of Kohn-Laplace equations on the Heisenberg group, 2007 (in preparation)Folland, G.B., (1989) Annals of Mathematics Studies, 122. , Princeton University Press, Princeton, NJFolland, G.B., Stein, E.M., Estimates for the over(∂, ̄)b complex and analysis on the Heisenberg group (1974) Comm. Pure Appl. Math., 27, pp. 429-522Garofalo, N., Lanconelli, E., Zero-order perturbations of the subelliptic Laplacian on the Heisenberg group and their uniqueness properties (1990) Bull. Amer. Math. Soc. (N.S.), 23, pp. 501-512Garofalo, N., Lanconelli, E., Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation (1990) Ann. Inst. Fourier (Grenoble), 40, pp. 313-356Garofalo, N., Lanconelli, E., Existence and nonexistence results for semilinear equations on the Heisenberg group (1992) Indiana Univ. Math. J., 41, pp. 71-98Hörmander, L., Hypoelliptic second order differential equations (1967) Acta Math., 119, pp. 147-171Howe, R., On the role of the Heisenberg group in harmonic analysis (1980) Bull. Amer. Math. Soc. (N.S.), 3, pp. 821-843Hueber, H., Müller, D., Asymptotics for some Green kernels on the Heisenberg group and the Martin boundary (1989) Math. Ann., 283, pp. 97-119Ibragimov, N.H., (1985) Transformation Groups Applied to Mathematical Physics, , D. Reidel Publishing Co., Dordrecht Translated from Russian Mathematics and its Applications (Soviet Series)Jerison, D.S., The Dirichlet problem for the Kohn Laplacian on the Heisenberg group. I (1981) J. Funct. Anal., 43, pp. 97-142Jerison, D.S., The Dirichlet problem for the Kohn Laplacian on the Heisenberg group. II (1981) J. Funct. Anal., 43, pp. 224-257Jerison, D.S., Lee, J.M., Intrinsic CR normal coordinates and the CR Yamabe problem (1989) J. Differential Geom., 29, pp. 303-343Jerison, D.S., Lee, J.M., Extremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem (1988) J. Amer. Math. Soc., 1, pp. 1-13Olver, P.J., (1986) GTM, 107. , Springer, New YorkOvsiannikov, L.V., (1982) Group Analysis of Differential Equations, , Academic Press, New York, London Translated from RussianPohozaev, S.I., Veron, L., Nonexistence results of solutions of semilinear differential inequalities on the Heisenberg group (2000) Manuscripta Math., 102, pp. 85-99Svirshchevskii, S.R., Group classification of nonlinear polyharmonic equations and their invariant solutions (1993) Differ. Equ., 29, pp. 1538-1547. , Differ. Uravn. 29 (10), 1772-1781 (in Russian
Existence of Multiple Solutions for Quasilinear Equations via Fibering Method
No full textAbstract. Existence and multiplicity results for a general class of radial qua- silinear equations are proved using the Fibering Method introduced and de- veloped by S. I. Pohozae
Lie Symmetries and Criticality of Semilinear Differential Systems
No full textWe discuss the notion of criticality of semilinear differential equations and systems, its relations to scaling transformations and the Noether approach to Pokhozhaev's identities. For this purpose we propose a definition for criticality based on the S. Lie symmetry theory. We show that this definition is compatible with the well-known notion of critical exponent by considering various examples. We also review some related recent papers.We wish to thank the referees for their useful suggestions. Yuri Bozhkov is grateful to the Organizers of the 7th International Conference “Symmetry in Nonlinear Mathematical Physics”, June 24–30 2007, Kyiv, Ukraine, for having given him the opportunity to present a talk on this subject. He would also like to thank FAPESP, CNPq and FAEPEX-UNICAMP, Brasil, as well as ICTP, Trieste, Italy, for financial support. Enzo Mitidieri acknowledges the support of INTAS-05-100000B-792
Conformal Killing Vector Fields And Rellich Type Identities On Riemannian Manifolds, Ii
No full textWe propose a general Noetherian approach to Rellich integral identities. Using this method we obtain a higher order Rellich type identity involving the polyharmonic operator on Riemannian manifolds admitting homothetic transformations. Then we prove a biharmonic Rellich identity in a more general context. We also establish a nonexistence result for semilinear systems involving biharmonic operators. © 2011 Springer Basel AG.91120Bozhkov, Y., Divergence symmetries of semilinear polyharmonic equations involving critical nonlinearities (2006) J. Differential Equations, 225, pp. 666-684Bozhkov, Y., A Caffarelli-Kohn-Nirenberg type inequality on Riemannian manifolds (2010) Applied Mathematics Letters, 23, pp. 1166-1169Bozhkov, Y., Freire, I.L., Special conformal groups of a Riemannian manifold and Lie point symmetries of the nonlinear Poisson Equation (2010) J. Differential Equations, 249, pp. 872-913Bozhkov, Y., Mitidieri, E., The Noether approach to Pohozaev's Identities (2007) Mediterr. J. Math., 4, pp. 383-405Bozhkov, Y., Mitidieri, E., Lie symmetries and criticality of semilinear differential systems (2007) SIGMA Symmetry, Integrability and Geometry: Methods and Applications, 3, p. 17. , Paper 053, (electronic)Bozhkov, Y., Mitidieri, E., Conformal Killing vector fields and Rellich type identities on Riemannian Manifolds (2008) I. Lecture Notes of Seminario Interdisciplinare Di Matematica, 7, pp. 65-80Clément, P., de Figueiredo, D., Mitidieri, E., Positive solutions of semilinear elliptic systems (1992) Comm. in Partial Differential Equations, 17 (5-6), pp. 923-940Ibragimov, N.H., Noether's identity (1979) Dinamika Sploshn. Sredy No., 38, pp. 26-32. , (Russian)Ibragimov, N.H., Transformation groups applied to mathematical physics (1985) Translated from the Russian Mathematics and its Applications, , (Soviet Series), D. Reidel Publishing Co., DordrechtMitidieri, E., (1990) A Rellich identity and applications, p. 35. , Rapporti interni n. 25, Univ. UdineMitidieri, E., A Rellich type identity and applications (1993) Commun. in Partial Differential Equations, 18 (1-2), pp. 125-151Mitidieri, E., Nonexistence of positive solutions of semilinear elliptic systems in ℝ N (1996) Differential Integral Equations, 9, pp. 465-479Mitidieri, E., A simple approach to Hardy inequalities (2000) Mat. Zametki, 67, pp. 563-572. , (In English: Math. Notes 67 (2000), 479 - 486.)Noether, E., Invariante Variationsprobleme. Nachrichten von der Kön. Ges. der Wissenschaften zu Göttingen (1918) Math.-Phys. Kl, (2), pp. 235-257. , (English translation in: Transport Theory and Statistical Physics 1(3), (1971), 186-207.)Olver, P., (1986) Applications of Lie Groups to Differential Equations, , New York: SpringerPohozaev, S.I., On the eigenfunctions of the equation Δu + λf(u) = 0 (1965) Dokl. Akad. Nauk SSSR, 165, pp. 36-39. , (In English: Soviet Math. Dokl. 6 (1965), 1408 - 1411.)Pohozaev, S.I., On eigenfunctions of quasilinear elliptic problems (1970) Mat. Sb, 82, pp. 192-212. , (In English: Math. USSR Sbornik 11 (1970), 171 - 188.)Pucci, P., Serrin, J., A general variational identity (1986) Indiana Univ. Math. J, 35 (3), pp. 681-703Rellich, F., Halbbeschränkte Differentialoperatoren höherer Ordnung (1954) Proceedings of the International Congress of Mathematicians, III, pp. 243-250. , Amsterdam, Erven P. Noordhoff N. V., GroningenNorth-Holland Publishing Co., 1956Yano, K., (1957) The theory of Lie derivatives and its applications, , North-Holland Publishing C
Spatially-localized time dependent solutions including turbulence and their interactions in 2D Kolmogorov flow
No full textIn 2D Kolmogorov flow in small aspect ratio domains, spatially-localized solutions such as kink, traveling or time-dependent kink-antikink pars coexist. However, the conservation of the flow rate in the y direction strongly restrict combination of localized solutions and their positioning. We find that by adding a homogeneous flow U y their positioning is controlled and each of localized solutions including a spatially-localized chaos is isolated. Numerical results suggest that these isolated solutions can be elements constructing a whole flow
Characteristics of overlap region in high-Reynolds number turbulent channel flow
No full textDirect numerical simulation of the fully developed turbulent channel flows have been carried out at the Reynolds number based on the friction velocity and the channel half width, 2000, 4000 and 8000. A hybrid 10th order accurate finite difference scheme in the stream and spanwise directions, and a second-order scheme in the wall-normal direction is adapted as the spatial discretization method. We observed the plateau profiles in the indicator function corresponded to the von Karman constant. Furthermore, second peak of streamwise pre-multiplied spectra were appeared in the same wall normal height, 300 < y+ < 600, in case of Re = 4000. Nevertheless, the effects of the lager than the channel half height scale on the streamwise turbulent intensity are fixed contributions without dependence on Reynolds number. These results suggested that the new streamwise vortexes are formed between buffer layer and outer layer with increasing of Reynolds number
La 'circunstancia' de 'Herederos y Pretendientes
No full textIn June 2010, the Ortega y Gasset Foundation hosted a Conference about the “Spanish Philosophical Transition” in order to debate the book of Francisco Vázquez, La filosofía española. Herederos y Pretendientes. Una lectura sociológica (1963-1990), recently published. This paper is the author’s response to criticism raised in the Conference and to published reviews received by this book. First, the author summarized the argument of Herederos y pretendientes. Secondly he responds and takes into account the most important objections against the book’s hypothesis and methodology. Finally the author evaluates the favorable judgments received by the book and suggests the limits of the historian’s task.Fundación Ortega y Gasset-Marañó
On The Lane-emden System In Dimension One
No full textWe carry out a complete group classification of the nonlinear Lane-Emden systems in dimension one. © 2012 Elsevier Inc. All rights reserved.218211076210766Bluman, G.W., Anco, S., (2002) Symmetry and Integration Methods for Differential Equations, , Springer New YorkBluman, G.W., Kumei, S., (1989) Symmetries and Differential Equations, 81. , Applied Mathematical Sciences Springer New YorkBokhari, A.H., Mahomed, F.M., Zaman, F.D., Symmetries and integrability of a fourth-order Euler-Bernoulli beam equation (2010) J. Math. Phys., 51, p. 053517Bozhkov, Y., Gilli Martins, A.C., Lie point symmetries of the Lane-Emden systems (2004) Journal of Mathematical Analysis and Applications, 294 (1), pp. 334-344. , DOI 10.1016/j.jmaa.2004.02.022, PII S0022247X04001532Bozhkov, Y., Freire, I.L., Symmetry analysis of the bidimensional Lane-Emden systems (2012) J. Math. Anal. Appl., 388, pp. 1279-1284. , 10.1016/j.jmaa.2011.11.024Bozhkov, Y., Freire, I.L., (2012) The Complete Group Classification of Lane-Emden Systems, , in preparationDai, Q., Tisdell, C., Nondegeneracy of positive solutions to homogeneous second-order differential systems and its applications (2009) Acta Math. Sci. Ser., 29, pp. 435-446Freire, I.L., Silva, P.L., Torrisi, M., Symmetry and Integrability of A Fourth-order Emden-Fowler Equation, , 2012 submitted for publicationIbragimov, N.H., (1985) Transformation Groups Applied to Mathematical Physics, , Translated from the Russian Mathematics and its Applications (Soviet Series) D. Reidel Publishing Co. DordrechtIbragimov, N.H., Integrating factors, adjoint equations and Lagrangians (2006) Journal of Mathematical Analysis and Applications, 318 (2), pp. 742-757. , DOI 10.1016/j.jmaa.2005.11.012, PII S0022247X05011546Ibragimov, N.H., A new conservation theorem (2007) J. Math. Anal. Appl., 333, pp. 311-328Muatjetjeja, B., Khalique, C.M., Lagrangian approach to a generalized coupled Lane-Emden system: Symmetries and first integrals (2010) Commun. Nonlinear Sci. Numer. Simulat., 15, pp. 1166-1171Muatjetjeja, B., Khalique, C.M., Noether partial Noether operators and first integrals for the coupled Lane-Emden system (2010) Math. Comput. Appl., 15, pp. 325-333Muatjetjeja, B., Khalique, C.M., First integrals for a generalized coupled Lane-Emden system (2011) Nonlinear Anal. Real World Appl., 12, pp. 1202-1212Olver, P.J., (1986) Applications of Lie Groups to Differential Equations, , Springer New Yor
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