Positive solutions of the \(p(x)\)-Laplace equation with singular nonlinearity

DOI10.1016/j.na.2010.02.018zbMath1189.35131OpenAlexW2029820905MaRDI QIDQ972395

Jingjing Liu

Publication date: 25 May 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.02.018

zbMATH Keywords

singular boundary value problemsub-supersolution method\(p(x)\)-Laplacian

Mathematics Subject Classification ID

Degenerate elliptic equations (35J70) Variational methods for second-order elliptic equations (35J20) Quasilinear elliptic equations (35J62) Positive solutions to PDEs (35B09) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (12)

A fractional \(p(x,\cdot)\)-Laplacian problem involving a singular term ⋮ A pocket guide to nonlinear differential equations in Musielak-Orlicz spaces ⋮ Existence results for singular double phase problem with variable exponents ⋮ On some singular problems involving the fractional p(x,.) -Laplace operator ⋮ Existence of a solution for some singular quasilinear problem with variable exponent and containing gradient term ⋮ Existence and multiplicity of solutions for a quasilinear equation involving thep(x)-Laplace operator ⋮ A multiplicity results for a singular equation involving thep(x)-Laplace operator ⋮ The fibering map approach for a singular elliptic system involving the $p(x)$-Laplacian and nonlinear boundary conditions ⋮ Liouville theorems for elliptic problems in variable exponent spaces ⋮ Existence of positive solutions to a class of \(p(x)\)-Laplacian equations with singular nonlinearities ⋮ A singular elliptic system involving the p(x)-Laplacian and generalized Lebesgue–Sobolev spaces ⋮ Critical \(p(x)\)-Kirchhoff problems involving variable singular exponent

Cites Work

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• On singular \(p\)-Laplacian problems
• On the sub-supersolution method for \(p(x)\)-Laplacian equations
• Positive solutions of the \(p\)-Laplace equation with singular nonlinearity
• Asymptotic behavior of solutions of boundary blow-up problems
• Eigenvalues of \(p(x)\)-Laplacian Dirichlet problem
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• A class of De Giorgi type and Hölder continuity
• Regularity results for a class of functionals with non-standard growth
• Variational and topological methods for Dirichlet problems with \(p\)-Laplacian
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)

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