Constant sign and nodal solutions for logistic-type equations with equidiffusive reaction

DOI10.1007/s00605-010-0257-1zbMath1235.35137OpenAlexW1975637367MaRDI QIDQ663346

Francesca Papalini, Nikolaos S. Papageorgiou

Publication date: 14 February 2012

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-010-0257-1

zbMATH Keywords

Morse theorycritical point theorytruncation techniqueslogistic-type equationsuperlinear nonlinearityequidiffusive reactionpositive and nodal solutions

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for second-order elliptic equations (35J20)

Related Items (8)

On p-logistic equations of equidiffusive type ⋮ Positive solutions of generalized nonlinear logistic equations via sub-super solutions ⋮ Existence, nonexistence and multiplicity of positive solutions for nonlinear, nonhomogeneous Neumann problems ⋮ Seven solutions with sign information for sublinear equations with unbounded and indefinite potential and no symmetries ⋮ Constant sign solutions for variable exponent system Neumann boundary value problems with singular coefficient ⋮ A variational approach to nonlinear logistic equations ⋮ On a Robin (p,q)-equation with a logistic reaction ⋮ On nodal solutions for nonlinear elliptic equations with a nonhomogeneous differential operator

Cites Work

• Unnamed Item
• Unnamed Item
• Construction of pseudo-gradient vector field and sign-changing multiple solutions involving \(p\)-Laplacian
• Multiplicity theorems for superlinear elliptic problems
• Multiple constant sign and nodal solutions for nonlinear elliptic equations with the \(p\)-Laplacian
• Critical point theory and Hamiltonian systems
• On the diffusion of biological populations
• Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results
• On a diffusive logistic equation
• Nontrivial critical groups in \(p\)-Laplacian problems via the Yang index
• On a superlinear elliptic \(p\)-Laplacian equation.
• Asymptotic properties of a reaction-diffusion equation with degenerate \(p\)-Laplacian
• Splitting theorem, Poincaré--Hopf theorem and jumping nonlinear problems
• Sign-changing and multiple solutions for the \(p\)-Laplacian
• A strong maximum principle for some quasilinear elliptic equations
• A degree theoretic approach for multiple solutions of constant sign for nonlinear elliptic equations
• Flat Core Properties Associated to the p-Laplace Operator
• Bifurcation Phenomena Associated to the p-Laplace Operator
• Quasilinear elliptic equations involving critical Sobolev exponents
• Positive solutions of a degenerate elliptic equation with logistic reaction
• On the global bifurcation diagram for the one-dimensional Ginzburg–Landau model of superconductivity
• Critical point theory for asymptotically quadratic functionals and applications to problems with resonance
• A PRIORI ESTIMATES AND EXISTENCE OF POSITIVE SOLUTIONS FOR A QUASILINEAR ELLIPTIC EQUATION
• Some remarks on the Fučík spectrum of the \(p\)-Laplacian and critical groups
• Multiplicity results for a degenerate elliptic equation with logistic reaction

This page was built for publication: Constant sign and nodal solutions for logistic-type equations with equidiffusive reaction