Critical points theorems via the generalized Ekeland variational principle and its application to equations of \(p(x)\)-Laplace type in \(\mathbb{R}^{N}\)

DOI10.11650/tjm/181004zbMath1409.58004OpenAlexW2896738905MaRDI QIDQ1722082

Yun-Ho Kim, Jung-Hyun Bae

Publication date: 14 February 2019

Published in: Taiwanese Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.twjm/1540195384

zbMATH Keywords

mountain pass theoremweak solutionsEkeland's variational principleCerami conditionvariable exponent Lebesgue-Sobolev spaces\(p(x)\)-Laplace type operatorcontinuously Gâteaux differentiable functionalscritical points theorems

Mathematics Subject Classification ID

Fréchet and Gateaux differentiability in optimization (49J50) Nonlinear elliptic equations (35J60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational principles in infinite-dimensional spaces (58E30) Second-order elliptic equations (35J15) Weak solutions to PDEs (35D30)

Related Items (6)

Existence, multiplicity and regularity of solutions for the fractional $p$-Laplacian equation ⋮ Existence and multiplicity of solutions for Schrödinger-Kirchhoff type problems involving the fractional \(p(\cdot) \)-Laplacian in \(\mathbb{R}^N\) ⋮ Existence and multiplicity of solutions to concave-convex-type double-phase problems with variable exponent ⋮ Homoclinic solutions for Hamiltonian systems of \(p\)-Laplacian-like type ⋮ Fractional Sobolev spaces with kernel function on compact Riemannian manifolds ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On some degenerate quasilinear equations involving variable exponents
• A critical point theorem via the Ekeland variational principle
• On superlinear \(p(x)\)-Laplacian problems without Ambrosetti and Rabinowitz condition
• Multiple solutions for an eigenvalue problem involving \(p\)-Laplacian type operators
• Existence and multiplicity of weak solutions for elliptic Dirichlet problems with variable exponent
• Lebesgue and Sobolev spaces with variable exponents
• A nondifferentiable extension of a theorem of Pucci and Serrin and applications
• Existence results for a Neumann problem involving the \(p(x)\)-Laplacian with discontinuous nonlinearities
• On a sub-supersolution method for variational inequalities with Leray-Lions operators in variable exponent spaces
• Superlinear problems without Ambrosetti and Rabinowitz growth condition
• The existence of a nontrivial solution to a nonlinear elliptic boundary value problem of \(p\)-Laplacian type without the Ambrosetti-Rabinowitz condition
• On superlinear \(p(x)\)-Laplacian equations in \(\mathbb R^N\)
• On Ekeland's variational principle and a minimax theorem
• On a three critical points theorem
• Electrorheological fluids: modeling and mathematical theory
• Infinitely many critical points of non-differentiable functions and applications to a Neumann-type problem involving the \(p\)-Laplacian
• Existence and multiplicity of solutions for equations of \(p(x)\)-Laplace type in \(\mathbb{R}^N\) without AR-condition.
• Critical points for multiple integrals of the calculus of variations
• On the variational principle
• Nontrivial solutions for perturbations of the \(p\)-Laplacian on unbounded domains
• A characterization of the mountain pass geometry for functionals bounded from below.
• A general variational principle and some of its applications
• Existence and multiplicity of solutions for equations involving nonhomogeneous operators of \(p(x)\)-Laplace type in \(\mathbb{R}^{N}\)
• Dual variational methods in critical point theory and applications
• Mountain pass type solutions and positivity of the infimum eigenvalue for quasilinear elliptic equations with variable exponents
• Existence and multiplicity results for elliptic problems with \(p(\cdot)\)-growth conditions
• A weak nonsmooth Palais-Smale condition and coercivity
• Relations between the mountain pass theorem and local minima
• Discontinuous elliptic problems involving the p(x)‐Laplacian
• Remarks on finding critical points
• On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on ℝ^N
• A generalization of Ekerland's variational principle and application to the study of the relation between the weak P.S. condition and coercivity
• Sobolev embeddings with variable exponent
• Infinitely many solutions for equations of p(x)-Laplace type with the nonlinear Neumann boundary condition
• On the structure of the critical set of non-differentiable functions with a weak compactness condition
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
• On a three critical points theorem for non-differentiable functions and applications to nonlinear boundary value problems

This page was built for publication: Critical points theorems via the generalized Ekeland variational principle and its application to equations of \(p(x)\)-Laplace type in \(\mathbb{R}^{N}\)