On a Parametric Nonlinear Dirichlet Problem with Subdiffusive and Equidiffusive Reaction

DOI10.1515/ans-2014-0303zbMath1408.35024OpenAlexW2515379527MaRDI QIDQ2923153

Patrick Winkert, Nikolaos S. Papageorgiou

Publication date: 15 October 2014

Published in: Advanced Nonlinear Studies (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ans-2014-0303

zbMATH Keywords

maximum principleextremal solutionslocal minimizersconstant sign and nodal solutionsnonlinear regularitycritical point of mountain pass type

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for second-order elliptic equations (35J20) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (16)

Infinitely many nodal solutions for nonlinear nonhomogeneous Robin problems ⋮ Positive solutions of generalized nonlinear logistic equations via sub-super solutions ⋮ Infinitely many nodal solutions for semilinear Robin problems with an indefinite linear part ⋮ On a class of parametric \((p,2)\)-equations ⋮ Existence, nonexistence and multiplicity of positive solutions for nonlinear, nonhomogeneous Neumann problems ⋮ Bounded weak solutions to superlinear Dirichlet double phase problems ⋮ Positive solutions for superdiffusive mixed problems ⋮ Multiplicity of solutions for nonlinear nonhomogeneous Robin problems ⋮ Multiple and nodal solutions for parametric Neumann problems with nonhomogeneous differential operator and critical growth ⋮ Anisotropic Robin problems with logistic reaction ⋮ Nonlinear Robin problems with a reaction of arbitrary growth ⋮ Existence and nonexistence of positive solutions for singular \((p, q)\)-equations with superdiffusive perturbation ⋮ Nonlinear Neumann problems with indefinite potential and concave terms ⋮ Infinitely many nodal solutions for generalized logistic equations without odd symmetry on reaction ⋮ On a Robin (p,q)-equation with a logistic reaction ⋮ Some existence and uniqueness results for logistic Choquard equations

Cites Work

• Positive solutions and bifurcation phenomena for nonlinear elliptic equations of logistic type: the superdiffusive case
• Counterexamples to some conjectures on the number of solutions of nonlinear equations
• Multiple solutions for nonlinear Neumann problems driven by a nonhomogeneous differential operator
• SOBOLEV VERSUS HÖLDER LOCAL MINIMIZERS AND GLOBAL MULTIPLICITY FOR SOME QUASILINEAR ELLIPTIC EQUATIONS
• Degree theory for operators of monotone type and nonlinear elliptic equations with inequality constraints

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