A variational approach to nonlinear logistic equations

DOI10.1142/S0219199714500217zbMath1318.35011OpenAlexW2163153798WikidataQ112251734 ScholiaQ112251734MaRDI QIDQ4983011

Leszek Gasiński, Nikolaos S. Papageorgiou, Donal O'Regan

Publication date: 14 April 2015

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219199714500217

zbMATH Keywords

maximum principlepositive solutionnonlinear regularity theorynonlinear logistic equationdegenerate logistic equation

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) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Positive solutions to PDEs (35B09) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items

Multiple constant sign and nodal solutions for nonlinear nonhomogeneous elliptic equations depending on a parameter, Positive solutions of generalized nonlinear logistic equations via sub-super solutions, Unnamed Item, Asymmetric \(8(p,2)\)-equations with double resonance, Positive solutions for nonlinear nonhomogeneous Robin problems, Unnamed Item, Positive solutions for the Robin \(p\)-Laplacian problem with competing nonlinearities, Multiple and nodal solutions for parametric Neumann problems with nonhomogeneous differential operator and critical growth, Existence and multiplicity results for generalized logistic equations, Existence results for some nonlinear elliptic equations via topological degree methods, Existence and nonexistence of positive solutions for singular \((p, q)\)-equations with superdiffusive perturbation, Infinitely many nodal solutions for generalized logistic equations without odd symmetry on reaction, Some existence and uniqueness results for logistic Choquard equations, Schrödinger Robin problems with indefinite potential and logistic reaction

Cites Work

• Unnamed Item
• Unnamed Item
• Combined effects in nonlinear problems arising in the study of anisotropic continuous media
• Constant sign and nodal solutions for logistic-type equations with equidiffusive reaction
• Multiple solutions for nonlinear coercive problems with a nonhomogeneous differential operator and a nonsmooth potential
• Nodal and multiple constant sign solutions for resonant \(p\)-Laplacian equations with a nonsmooth potential
• Continuous selections. I
• The maximum principle
• Handbook of applied analysis
• Existence of five nonzero solutions with exact sign for a \(p\)-Laplacian equation
• Scalar curvature and conformal deformation of Riemannian structure
• On the diffusion of biological populations
• On a diffusive logistic equation
• Solitons in several space dimensions: Derrick's problem and infinitely many solutions
• A note on a result of Ambrosetti and Mancini
• The beginning of the Fučik spectrum for the \(p\)-Laplacian
• A strong maximum principle for some quasilinear elliptic equations
• Multiplicity theorems for scalar periodic problems at resonance with \(p\)-Laplacian-like operator
• Variational and non-variational eigenvalues of the \(p\)-Laplacian
• Linear and quasilinear elliptic equations
• Multiplicity theorems for periodic systems with a \(p\)-Laplacian-like operator
• On a class of nonlinear dirichlet problems with multiple solutions
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• Sharp nonuniqueness results for some nonlinear problems
• On the Positive Solutions of Semilinear Equations Δu + λu - hu p = 0 on the Compact Manifolds
• The natural generalizationj of the natural conditions of ladyzhenskaya and uralľtseva for elliptic equations
• The Ambrosetti–Prodi Problem for thep-Laplace Operator
• Critical point theory for asymptotically quadratic functionals and applications to problems with resonance
• A multiplicity theorem for problems with the \(p\)-Laplacian
• Critical point theory on partially ordered Hilbert spaces