Existence of solutions for a Kirchhoff problem involving p(x) - biharmonic operator
Cumhuriyet Science JournalThis article is dealt with a Kirchhoff problem involving p(x) - biharmonic operator. By means of the Variational method and Ekeland’s variational principle, we establish the existence of a nontrivial weak solution in Sobolev spaces with variable exponent
Zehra Yücedağ, İlknur Gürbüz
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Existence and multiplicity of weak solutions for a class of degenerate nonlinear elliptic equations
Boundary Value Problems, 2006 The goal of this paper is to study the existence and the multiplicity of non-trivial weak solutions for some degenerate nonlinear elliptic equations on the whole space RN. The solutions will be obtained in a subspace of the Sobolev space W1/p(RN).
Mihai Mihăilescu
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Applications of Ekeland's principle to locally Lipschitzian functionals
, 2000 We prove an extension of a complement to Ekeland's variational principle for functionals whose domain is a particular subset of a Banach space.
STURIALE G. +2 more
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Hoelder stability, Solution schemes and Ekeland's principle [PDF]
, 2011 We present two basic lemmas on exact and approximate solutions of inclusions and equations in general spaces. Its applications involve Ekeland’s principle, characterize calmness, lower semicontinuity and the Aubin property of solution sets in some ...
Kummer, Bernd
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Positive Solutions for a Nonhomogeneous Kirchhoff Equation with the Asymptotical Nonlinearity in R3
Abstract and Applied Analysis, 2014 We study the following nonhomogeneous Kirchhoff equation: -(a+b∫R3|∇u|2dx)Δu+u=k(x)f(u)+h(x), x∈R3, u∈H1(R3), u>0, x∈R3, where f is asymptotically linear with respect to t at infinity.
Ling Ding, Lin Li, Jin-Ling Zhang
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The Ekeland's Variational Principle
, 2022 The present work has as target audience all students who have experience in Real Analysis. Some introductory results of Functional Analysis will be presented, as some definitions and results in metric spaces, having as main result: Ekeland’s ...
Azevedo, Mateus Vinicius Santos de
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A maximum principle for nonsmooth optimal-control problems with state constraints [PDF]
, 1982 Optimality conditions are derived in the form of a maximum principle governing solutions to an optimal control problem which involves state constraints.
Vinter, R.B, Pappas, G
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Le Matematiche, 2006 A drop theorem on ordered metric spaces is established from the (pre) order version of Ekeland’s variational principle in Turinici [An St UAIC Ia (Math), 36 (1990), 329-352]. The logical equivalence between these results is also discussed.
Mihai Turinici
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Minimal element theorems and Ekeland's variational principle with new set order relations
, 2018 By using scalarization functions, we study minimal element theorem, Ekeland's variational principle, Caristi's fixed point theorem, Takahashi's minimization theorem under the set order relations on the family of sets defined by means of Minkowski ...
Yao, Jen Chih +2 more
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An extension of Pontryagin's principle for state-constrained optimal control of semilinear elliptic equations and variational inequalities [PDF]
, 1992 Projet PROMATHThis paper deals with state-constrained optimal control problems governed by semilinear elliptic equations or variational inequalities. By using Ekeland's principle, we derive a minimum principle of Pontryagin's type under some stability ...
Casas, Eduardo, Bonnans, J. Frederic
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