Qualitative phenomena for some classes of quasilinear elliptic equations with multiple resonance

DOI10.1007/s00245-013-9227-zzbMath1304.35077OpenAlexW2110906188MaRDI QIDQ742150

Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu

Publication date: 18 September 2014

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00245-013-9227-z

zbMATH Keywords

critical groupstrong comparison principlenonlinear maximum principleresonant equationsLyapunoff-Schmidt reduction methodnodal and constant sign solutions

Mathematics Subject Classification ID

Resonance in context of PDEs (35B34) Quasilinear elliptic equations with (p)-Laplacian (35J92) Comparison principles in context of PDEs (35B51)

Related Items (57)

Asymmetric \((p,2)\)-equations, superlinear at \(+\infty\) resonant at \(-\infty\) ⋮ Quasilinear Schrödinger equations with bounded coefficients ⋮ Infinitely many nodal solutions for nonlinear nonhomogeneous Robin problems ⋮ Existence of solution for a resonant \(p\)-Laplacian second-order \(m\)-point boundary value problem on the half-line with two dimensional kernel ⋮ Multiple solutions for a coercive quasilinear elliptic equation via Morse theory ⋮ The Brezis-Oswald result for quasilinear Robin problems ⋮ Nonlinear elliptic equations with a jumping reaction ⋮ Nonlinear nonhomogeneous Robin problems with superlinear reaction term ⋮ On noncoercive \((p, q)\)-equations ⋮ \((p,2)\)-equations asymmetric at both zero and infinity ⋮ On a class of parametric \((p,2)\)-equations ⋮ Multiple solutions for resonant problems of the Robin \(p\)-Laplacian plus an indefinite potential ⋮ Asymmetric \(8(p,2)\)-equations with double resonance ⋮ Existence, nonexistence and multiplicity of positive solutions for nonlinear, nonhomogeneous Neumann problems ⋮ Global strong solution of fourth order nonlinear wave equation ⋮ Nonlinear, nonhomogeneous Robin problems with indefinite potential and general reaction ⋮ Multiplicity results for nonlinear nonhomogeneous Robin problems with indefinite potential term ⋮ Nonhomogeneous hemivariational inequalities with indefinite potential and Robin boundary condition ⋮ Positive solutions for parametric singular Dirichlet \(( p, q)\)-equations ⋮ Multiple solutions for \((p,2)\)-equations with resonance and concave terms ⋮ A multiplicity theorem for parametric superlinear (p,q)-equations ⋮ Multiplicity of solutions for nonlinear nonhomogeneous Robin problems ⋮ Nonlinear Nonhomogeneous Elliptic Problems ⋮ (p,2)-equations resonant at any variational eigenvalue ⋮ Resonant-superlinear and resonant-sublinear Dirichlet problems ⋮ Double-phase problems and a discontinuity property of the spectrum ⋮ Nodal solutions for nonlinear nonhomogeneous Robin problems ⋮ Multiple solutions for \((p, 2)\)-equations at resonance ⋮ Nonlinear eigenvalue problems for the \((p,q)\)-Laplacian ⋮ On noncoercive elliptic problems ⋮ Multiple solutions with sign information for a \(( p, 2)\)-equation with combined nonlinearities ⋮ Global well-posedness, asymptotic behavior and blow-up of solutions for a class of degenerate parabolic equations ⋮ Arbitrarily positive initial energy blowup and blowup time for some fourth-order viscous wave equation ⋮ Multiple solutions with sign information for a class of coercive \((p, 2)\)-equations ⋮ Existence and multiplicity of solutions for resonant \((p,2)\)-equations ⋮ Sign-changing solutions for resonant and superlinear nonhomogeneous elliptic equations ⋮ Positive solutions for nonlinear nonhomogeneous parametric Robin problems ⋮ Noncoercive resonant \((p,2)\)-equations ⋮ Double-phase problems with reaction of arbitrary growth ⋮ Nonlinear nonhomogeneous singular problems ⋮ Unbalanced \((p,2)\)-fractional problems with critical growth ⋮ Solutions and positive solutions for superlinear Robin problems ⋮ Multiple solutions with sign information for a class of parametric superlinear \((p, 2)\)-equations ⋮ Nonlinear Neumann problems with indefinite potential and concave terms ⋮ \((p, 2)\)-equations with a crossing nonlinearity and concave terms ⋮ Existence of continuous eigenvalues for a class of parametric problems involving the \((p,2)\)-Laplacian operator ⋮ Infinitely many nodal solutions for nonlinear elliptic equations with combined nonlinearities and lack of symmetry ⋮ Hyperbolic and parabolic equations with several opposite-sign source at critical initial energy level in heat and vibrating systems ⋮ Nodal Solutions for Nonlinear Non-Homogeneous Robin Problems with an Indefinite Potential ⋮ Noncoercive resonant \((p,2)\)-equations with concave terms ⋮ Constant sign and nodal solutions for parametric \((p, 2)\)-equations ⋮ Unnamed Item ⋮ Positive Solutions for Parametric Nonlinear Nonhomogeneous Robin Problems ⋮ Nonlinear nonhomogeneous boundary value problems with competition phenomena ⋮ Three solutions for parametric problems with nonhomogeneous \((a,2)\)-type differential operators and reaction terms sublinear at zero ⋮ Critical groups at zero and multiple solutions for a quasilinear elliptic equation ⋮ Bifurcation of positive solutions for nonlinear nonhomogeneous Robin and Neumann problems with competing nonlinearities

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