Existence and multiplicity of solutions for equations involving nonhomogeneous operators of \(p(x)\)-Laplace type in \(\mathbb{R}^{N}\)

DOI10.1186/S13661-014-0261-9zbMath1316.35139OpenAlexW2143945507WikidataQ59320054 ScholiaQ59320054MaRDI QIDQ2263526

Kisoeb Park, Seung Dae Lee, Yun-Ho Kim

Publication date: 18 March 2015

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13661-014-0261-9

zbMATH Keywords

weak solutionmountain pass theoremFountain theorem\(p(x)\)-Laplace typevariable exponent Lebesgue-Sobolev spaces

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Weak solutions to PDEs (35D30) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (10)

Existence and multiplicity of positive solutions to quasilinear elliptic equations with two parameters ⋮ Multiplicity results for nonlinear Neumann boundary value problems involving \(p\)-Laplace type operators ⋮ Radially symmetric solutions for quasilinear elliptic equations involving nonhomogeneous operators in an Orlicz-Sobolev space setting ⋮ Existence of three solutions for equations of \(p(x)\)-Laplace type operators with nonlinear Neumann boundary conditions ⋮ Homoclinic solutions for Hamiltonian systems of \(p\)-Laplacian-like type ⋮ Critical points theorems via the generalized Ekeland variational principle and its application to equations of \(p(x)\)-Laplace type in \(\mathbb{R}^{N}\) ⋮ Existence and multiplicity of solutions for Kirchhoff-Schrödinger type equations involving \(p(x)\)-Laplacian on the entire space \(\mathbb{R}^N\) ⋮ The existence of infinitely many solutions for nonlinear elliptic equations involving p-Laplace type operators in R^N ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Infinitely many solutions for elliptic problems with variable exponent and nonlinear boundary conditions
• Multiple solutions for an eigenvalue problem involving \(p\)-Laplacian type operators
• Lebesgue and Sobolev spaces with variable exponents
• On a sub-supersolution method for variational inequalities with Leray-Lions operators in variable exponent spaces
• Electrorheological fluids: modeling and mathematical theory
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• Existence and multiplicity of solutions for \(p(x)\)-Laplacian equations in \(\mathbb R^N\)
• Minimax theorems
• Positivity of the infimum eigenvalue for equations of \(p(x)\)-Laplace type in \(\mathbb R^N\)
• Mountain pass type solutions and positivity of the infimum eigenvalue for quasilinear elliptic equations with variable exponents
• Density of smooth functions in W ^{k, p(x)} ( Ω )
• Sobolev embeddings for unbounded domain with variable exponent having values across N
• On a nonhomogeneous quasilinear eigenvalue problem in Sobolev spaces with variable exponent
• A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)

This page was built for publication: Existence and multiplicity of solutions for equations involving nonhomogeneous operators of \(p(x)\)-Laplace type in \(\mathbb{R}^{N}\)