Multiple constant sign and nodal solutions for nonlinear elliptic equations with the \(p\)-Laplacian

DOI10.1016/j.jde.2008.07.004zbMath1151.35036OpenAlexW1967936251MaRDI QIDQ947143

Nikolaos S. Papageorgiou, Michael E. Filippakis

Publication date: 29 September 2008

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.07.004

zbMATH Keywords

\(p\)-Laplaciannodal solutionsupper-lower solutionconstant sign solutionsconcave-convex nonlinearitysecond deformation theoremtruncated functional

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Degenerate elliptic equations (35J70) Variational methods for second-order elliptic equations (35J20)

Related Items (54)

Robin problems with a general potential and a superlinear reaction ⋮ Infinitely many nodal solutions for nonlinear nonhomogeneous Robin problems ⋮ Existence of infinitely many solutions for a \(p\)-Kirchhoff problem in RN ⋮ Singular \(p\)-Laplacian equations with superlinear perturbation ⋮ On a Dirichlet problem with \((p,q)\)-Laplacian and parametric concave-convex nonlinearity ⋮ Nonlinear noncoercive Neumann problems ⋮ A multiplicity result for some Kirchhoff-type equations involving exponential growth condition in \(\mathbb{R}^2 \) ⋮ Positive and nodal solutions for parametric nonlinear Robin problems with indefinite potential ⋮ Infinitely many sign-changing solutions to some quasilinear equation involving exponential term ⋮ On noncoercive \((p, q)\)-equations ⋮ Multiple solutions for nonlinear nonhomogeneous resonant coercive problems ⋮ Nodal solutions for the Robin \(p\)-Laplacian plus an indefinite potential and a general reaction term ⋮ Multiple solutions to some degenerate quasilinear equation with variable exponents via perturbation method ⋮ Nonhomogeneous hemivariational inequalities with indefinite potential and Robin boundary condition ⋮ Constant sign and nodal solutions for resonant double phase problems ⋮ Solutions with sign information for noncoercive double phase equations ⋮ Multiple solutions for \((p,2)\)-equations with resonance and concave terms ⋮ Sign-changing solutions for parametric Neumann problems with broken symmetry and arbitrary growth ⋮ Anisotropic \((p, q)\)-equations with asymmetric reaction term ⋮ On an anisotropic eigenvalue problem ⋮ Nonautonomous \((p,q)\)-equations with unbalanced growth and competing nonlinearities ⋮ Positive solutions for nonlinear singular problems with sign-changing nonlinearities ⋮ Anisotropic equations with indefinite potential and competing nonlinearities ⋮ Positive solutions for the Robin \(p\)-Laplacian problem with competing nonlinearities ⋮ Unnamed Item ⋮ Perturbed eigenvalue problems for the Robin \(p\)-Laplacian plus an indefinite potential ⋮ Nonlinear elliptic equations with an asymptotically linear reaction term ⋮ Constant sign and nodal solutions for logistic-type equations with equidiffusive reaction ⋮ Multiple solutions for \((p, 2)\)-equations at resonance ⋮ Positive solutions for \((p, q)\)-equations with convection and a sign-changing reaction ⋮ Multiple solutions with sign information for a \(( p, 2)\)-equation with combined nonlinearities ⋮ Multiple solutions with sign information for a class of coercive \((p, 2)\)-equations ⋮ Existence and multiplicity of solutions for resonant \((p,2)\)-equations ⋮ MULTIPLICITY OF SOLUTIONS FOR SEMILINEAR ELLIPTIC PROBLEMS WITH COMBINED NONLINEARITIES ⋮ Positive solutions for nonlinear nonhomogeneous parametric Robin problems ⋮ Noncoercive resonant \((p,2)\)-equations ⋮ Positive solutions for perturbations of the Robin eigenvalue problem plus an indefinite potential ⋮ Double-phase problems with reaction of arbitrary growth ⋮ Robin problems with indefinite linear part and competition phenomena ⋮ Nonlinear nonhomogeneous singular problems ⋮ Unnamed Item ⋮ Extremal constant sign solutions and nodal solutions for the fractional \(p\)-Laplacian ⋮ Multiple solutions with sign information for a class of parametric superlinear \((p, 2)\)-equations ⋮ Positive solutions for parametric \((p(z),q(z))\)-equations ⋮ Unnamed Item ⋮ Infinitely many nodal solutions for generalized logistic equations without odd symmetry on reaction ⋮ Noncoercive resonant \((p,2)\)-equations with concave terms ⋮ Continuity results for parametric nonlinear singular Dirichlet problems ⋮ Constant sign and nodal solutions for parametric \((p, 2)\)-equations ⋮ Constant sign and nodal solutions for problems with the \(p\)-Laplacian and a nonsmooth potential using variational techniques ⋮ Nonlinear nonhomogeneous boundary value problems with competition phenomena ⋮ Multiple positive solutions for a \((p,q)\)-Laplace equation involving singular and critical terms ⋮ Nonlinear singular problems with indefinite potential and a superlinear perturbation ⋮ Robin problems with indefinite, unbounded potential and reaction of arbitrary growth

Cites Work

• Construction of pseudo-gradient vector field and sign-changing multiple solutions involving \(p\)-Laplacian
• On the antimaximum principle for the \(p\)-Laplacian with indefinite weight
• Multiple solutions for coercive \(p\)-Laplacian equations
• Existence and multiplicity results for Dirichlet problems with \(p\)-Laplacian.
• On a superlinear elliptic \(p\)-Laplacian equation.
• Infinite dimensional Morse theory and multiple solution problems
• On sign-changing and multiple solutions of the \(p\)-Laplacian.
• Multiplicity results for some nonlinear elliptic equations
• The beginning of the Fučik spectrum for the \(p\)-Laplacian
• A general variational principle and some of its applications
• A strong maximum principle for some quasilinear elliptic equations
• Absolute continuity on tracks and mappings of Sobolev spaces
• Quasilinear elliptic equations involving critical Sobolev exponents
• Boundary regularity for solutions of degenerate elliptic equations
• SOBOLEV VERSUS HÖLDER LOCAL MINIMIZERS AND GLOBAL MULTIPLICITY FOR SOME QUASILINEAR ELLIPTIC EQUATIONS
• Infinitely many arbitrarily small positive solutions for the Dirichlet problem involving the p-Laplacian
• A Dirichlet problem involving critical exponents
• On sign-changing solutions of certain semilinear elliptic problems
• Multiple nontrivial solutions for nonlinear eigenvalue problems
• THE EXISTENCE OF MULTIPLE SOLUTIONS TO QUASILINEAR ELLIPTIC EQUATIONS
• A multiplicity theorem for problems with the \(p\)-Laplacian
• Unnamed Item
• Unnamed Item
• Unnamed Item

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