Multiple solutions for elliptic systems via trapping regions and related nonsmooth potentials

DOI10.1080/00036811.2014.940520zbMath1325.35040OpenAlexW1977191087WikidataQ58295656 ScholiaQ58295656MaRDI QIDQ5264232

Motreanu, Dumitru, Siegfried Carl

Publication date: 24 July 2015

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2014.940520

zbMATH Keywords

quasilinear elliptic systemcomparison principlecritical pointmaximal solutionsign-changing solutionminimal solutionnonsmooth potentialsecond deformation lemmatrapping region

Mathematics Subject Classification ID

Variational methods for elliptic systems (35J50) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Quasilinear elliptic equations with (p)-Laplacian (35J92) Boundary value problems for second-order elliptic systems (35J57)

Related Items (7)

\(\mathcal{D}^{1,2}(\mathbb{R}^N)\) versus \(C(\mathbb{R}^N)\) local minimizer and a Hopf-type maximum principle ⋮ \(\mathcal{D}^{1,2}(\mathbb{R}^N)\) versus \(C(\mathbb{R}^N)\) local minimizer on manifolds and multiple solutions for zero-mass equations in \(\mathbb{R}^N\) ⋮ Existence and uniqueness of elliptic systems with double phase operators and convection terms ⋮ Doubly coupled systems of parabolic hemivariational inequalities: existence and extremal solutions ⋮ Doubly coupled systems of elliptic hemivariational inequalities: existence and location ⋮ Extremal solutions for nonvariational quasilinear elliptic systems via expanding trapping regions ⋮ Multiple solutions for nonvariational quasilinear elliptic systems

Cites Work

• Constant sign and sign changing solutions for systems of quasilinear elliptic equations
• On the multiple existence of semi-positive solutions for a nonlinear Schrödinger system
• The beginning of the Fučik spectrum for the \(p\)-Laplacian
• A strong maximum principle for some quasilinear elliptic equations
• A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system
• Constant-sign and sign-changing solutions for nonlinear eigenvalue problems
• Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems
• Fixed Point Theory in Ordered Sets and Applications
• Variational approach to noncoercive systems of elliptic variational inequalities via trapping region†
• Addendum to: Variational approach to noncoercive systems of elliptic variational inequalities via trapping region
• Boundary regularity for solutions of degenerate elliptic equations

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