1,720,966 research outputs found
On the existence of stationary solutions for higher-order p-Kirchhoff problems
No full textIn this paper, we establish the existence of two nontrivial weak solutions of possibly degenerate nonlinear eigenvalue problems involving the p-polyharmonic Kirchhoff operator in bounded domains. The p-polyharmonic operators ΔpL were recently introduced in [F. Colasuonno and P. Pucci, Multiplicity of solutions for p(x)-polyharmonic elliptic Kirchhoff equations, Nonlinear Anal. 74 (2011) 5962-5974] for all orders L and independently, in the same volume of the journal, in [V. F. Lubyshev, Multiple solutions of an even-order nonlinear problem with convex-concave nonlinearity, Nonlinear Anal. 74 (2011) 1345-1354] only for L even. In Sec. 3, the results are then extended to nondegenerate p(x)-polyharmonic Kirchhoff operators. The main tool of the paper is a three critical points theorem given in [F. Colasuonno, P. Pucci and Cs. Varga, Multiple solutions for an eigenvalue problem involving p-Laplacian type operators, Nonlinear Anal. 75 (2012) 4496-4512]. Several useful properties of the underlying functional solution space [W 0L,p (Ω)]d, endowed with the natural norm arising from the variational structure of the problem, are also proved both in the homogeneous case p ≡ Const. and in the non-homogeneous case p = p(x). In the latter some sufficient conditions on the variable exponent p are given to prove the positivity of the infimum λ1 of the Rayleigh quotient for the p(x)-polyharmonic operator Δp(x)L
A P-laplacian Neumann problem with a possibly supercritical nonlinearity
No full textWe look for nonconstant, positive, radial, radially nondecreasing solutions of the quasilinear equation-Δpu + up-1 = f(u) with p > 2, in the unit ball B of ℝN, subject to homogeneous Neumann boundary conditions. The assumptions on the nonlinearity f are very mild and allow it to be possibly supercritical in the sense of Sobolev embeddings. The main tools used are the truncation method and a mountain pass-type argument. In the pure power case, i.e. f(u) = uq-1, we detect the limit profile of the solutions of the problems as q → ∞. These results are proved in [3], in collaboration with B. Noris.SCOPUS: cp.jinfo:eu-repo/semantics/publishe
Lifespan estimates for solutions of polyharmonic Kirchhoff systems
No full textIn mathematical physics we increasingly encounter PDEs models connected with vibration problems for elastic bodies and deformation processes, as it happens in the Kirchhoff-Love theory for thin plates subjected to forces and moments. Recently Monneanu proved in Refs. 26 and 27 the existence of a solution of the nonlinear Kirchhoff-Love plate model. In this paper we treat several questions about non-continuation for maximal solutions of polyharmonic Kirchhoff systems, governed by time-dependent nonlinear dissipative and driving forces. In particular, we are interested in the strongly damped Kirchhoff-Love model, containing also an intrinsic dissipative term of Kelvin-Voigt type. Global non-existence and a priori estimates for the lifespan of maximal solutions are proved. Several applications are also presented in special subcases of the source term f and the nonlinear external damping Q. © 2012 World Scientific Publishing Company
Symmetry in the composite plate problem
Full text linkIn this paper, we deal with the composite plate problem, namely the following optimization eigenvalue problem: equation presented where P is a class of admissible densities, W = H 20 (Ω) for Dirichlet boundary conditions and W = H 2 (Ω) ∩ H 10 (Ω) for Navier boundary conditions. The associated Euler- Lagrange equation is a fourth-order elliptic PDE governed by the biharmonic operator Δ 2 . In the spirit of [S. Chanillo, D. Grieser, M. Imai, K. Kurata and I. Ohnishi, Symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes, Comm. Math. Phys. 214 (2000) 315-337], we study qualitative properties of the optimal pairs (u, ρ). In particular, we prove existence and regularity and we find the explicit expression of ρ.When Ω is a ball, we can also prove uniqueness of the optimal pair, as well as positivity of u and radial symmetry of both u and ρ
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Blow up at infinity of solutions of polyharmonic Kirchhoff systems
No full textThis article concerns the blow up at infinity of global solutions of strongly damped polyharmonic Kirchhoff systems, involving lower order terms, a time dependent nonlinear dissipative function Q and a driving force f, under homogeneous Dirichlet boundary conditions. Some applications are presented in special subcases of f and Q. © 2012 Copyright Taylor and Francis Group, LLC
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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