125,896 research outputs found
EXISTENCE, NONEXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS FOR PARAMETRIC NONLINEAR ELLIPTIC EQUATIONS
No full textWe consider a parametric nonlinear elliptic equation driven by the Dirichlet p-Laplacian. We study the existence, nonexistence and multiplicity of positive solutions as the parameter λ varies in R_0^+ and the potential exhibits a p-superlinear growth, without satisfying the usual in such cases Ambrosetti–Rabinowitz condition. We prove a bifurcation-type result when the reaction has (p - 1)-sublinear terms near zero (problem with concave and convex nonlinearities). We show that a similar bifurcation-type result is also true, if near zero the right hand side is (p - 1)-linear
Periodic problems and problems with discontinuities for nonlinear parabolic equations
No full textsummary:In this paper we study nonlinear parabolic equations using the method of upper and lower solutions. Using truncation and penalization techniques and results from the theory of operators of monotone type, we prove the existence of a periodic solution between an upper and a lower solution. Then with some monotonicity conditions we prove the existence of extremal solutions in the order interval defined by an upper and a lower solution. Finally we consider problems with discontinuities and we show that their solution set is a compact -set in
Investing in Hedge Funds: Risks, Returns, and Performance Measurement
No full textEdited by Greg N. Gregoriou, Georges Hübner, Nicolas Papageorgiou, Fabrice D. Rouah</p
Positive solutions for generalized nonlinear logistic equations of superdiffusive type
No full textWe consider a generalized version of the p-logistic equation. Using variational methods based on the critical point theory and truncation techniques, we prove a bifurcation-type theorem for the equation. So, we show that there is a critical value lambda*> 0 of the parameter lambda> 0 such that the following holds: if lambda> lambda*, then the problem has two positive solutions; if lambda= lambda*, then there is a positive solution; and finally, if 0 < lambda< lambda*, then there are no positive solutions
Existence and Relaxation for Finite-Dimensional Optimal Control Problems Driven by Maximal Monotone Operators
No full textIn this paper we study the optimal control of a class of nonlinear finite-dimensional optimal control problems driven by a maximal monotone operator which is not necessarily everywhere defined. So our model problem incorporates systems monitored by variational inequalities. First we prove an existence theorem using the reduction method of Berkovitz and Cesari. This requires a convexity hypothesis. When this convexity condition is not satisfied, we have to pass to an augmented, convexified problem known as the "relaxed problem". We present four relaxation methods. The first uses Young measures, the second uses multi-valued dynamics, the third is based on Caratheodory's theorem for convex sets in R-N and the fourth uses lower semicontinuity arguments and Gamma-limits. We show that they are equivalent and admissible, which roughly speaking means that the corresponding relaxed problem is in a sense the "closure" of the original one
Existence of two solutions for quasilinear periodic differential equations with discontinuities
No full textsummary:In this paper we examine a quasilinear periodic problem driven by the one- dimensional -Laplacian and with discontinuous forcing term . By filling in the gaps at the discontinuity points of we pass to a multivalued periodic problem. For this second order nonlinear periodic differential inclusion, using variational arguments, techniques from the theory of nonlinear operators of monotone type and the method of upper and lower solutions, we prove the existence of at least two non trivial solutions, one positive, the other negative
P. N. Papageorgiou, Ἡ ἐν Θεσσαλονίκῃ μονῇ τῶν Βλαταίων καὶ τὰ μετόχια αὐτῆς.
No full textPetit L. P. N. Papageorgiou, Ἡ ἐν Θεσσαλονίκῃ μονῇ τῶν Βλαταίων καὶ τὰ μετόχια αὐτῆς.. In: Échos d'Orient, tome 3, n°2, 1899. p. 128
P. N. Papageorgiou, Ἡ ἐν Θεσσαλονίκῃ μονῇ τῶν Βλαταίων καὶ τὰ μετόχια αὐτῆς.
No full textPetit L. P. N. Papageorgiou, Ἡ ἐν Θεσσαλονίκῃ μονῇ τῶν Βλαταίων καὶ τὰ μετόχια αὐτῆς.. In: Échos d'Orient, tome 3, n°2, 1899. p. 128
Multiple solutions for nonlinear periodic systems with combined nonlinearities and a nonsmooth potential
No full textWe consider nonlinear periodic systems driven by the p-Laplacian
and with a nonsmooth locally Lipschitz potential function. In the
right hand side forcing term, we have the combined effects of
p-sublinear (concave) and p-superlinear (convex) terms. However,
the p-superlinear term need not satisfy the Ambrosetti-Rabinowitz
condition. By combining nonsmooth critical point theory with the
Ekeland variational principle, we show that the system has at
least two nontrivial periodic solutions
Hammerstein integral inclusions in reflexive Banach spaces
No full textIn this paper we examine multivalued Hammerstein integral equations defined in a separable reflexive Banach space.We prove existence theorems for both the ‘convex’ problem (the
multifunction is convex-valued) and the ‘nonconvex’ problem (the multifunction is not necessarily convex-valued). We also show that the solution set of the latter is dense in the solution set of the former (relaxation theorem). Finally, we present some examples illustrating the applicability of
our abstract results
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