Positive and negative solutions of a quasi-linear elliptic equation by a mountain pass method and truncature techniques

DOI10.1016/j.na.2004.04.014zbMath1076.35035OpenAlexW2107762605MaRDI QIDQ1887983

Mario Girardi, Michele Matzeu

Publication date: 22 November 2004

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2004.04.014

zbMATH Keywords

iterationtruncationquasilinear elliptic equationmountain pass theorem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear elliptic equations (35J60) Variational methods for second-order elliptic equations (35J20)

Related Items

Nonzero positive solutions of elliptic systems with gradient dependence and functional BCs, Nonlinear nonhomogeneous Robin problems with dependence on the gradient, Existence of solution to Kirchhoff type problem with gradient nonlinearity and a perturbation term, Periodic solutions for extended Fisher-Kolmogorov and Swift-Hohenberg equations by truncature techniques, Nonlinear elliptic inclusions with unilateral constraint and dependence on the gradient, Positive solutions for a nonlocal problem with a convection term and small perturbations, Positive solutions for nonlinear Dirichlet problems with convection, Existence of periodic solutions for some second order quasilinear Hamiltonian systems, Robin problems for the \(p\)-Laplacian with gradient dependence, On fourth-order elliptic equations of Kirchhoff type with dependence on the gradient and the Laplacian, Positive solutions for nonlinear elliptic problems with dependence on the gradient, Semilinear elliptic variational inequalities with dependence on the gradient via mountain pass techniques, Existence of solutions for a bi-nonlocal fractional \(p\)-Kirchhoff type problem, Existence of solutions for fourth order elliptic equations of Kirchhoff type, Existence of positive solutions for the \(p\)-Laplacian with \(p\)-gradient term, A semilinear elliptic PDE not in divergence form via variational methods, Stability for semilinear elliptic variational inequalities depending on the gradient, Semi-linear singular elliptic equations with dependence on the gradient, Unnamed Item, Multiple solutions with sign information for semilinear Neumann problems with convection, Existence of positive solutions for nonlinear Robin problems with gradient dependence, Nonlinear nonhomogeneous Robin problems with convection, Positive solutions for nonlinear Neumann problems with singular terms and convection, Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Semilinear elliptic equations with dependence on the gradient via mountain-pass techniques.
• Existence of multiple solutions to nonlinear elliptic equations of nondivergence form
• Dual variational methods in critical point theory and applications
• Some existence theorems for equations of the form
• $L^\infty $ Estimate for Some Nonlinear Elliptic Partial Differential Equations and Application to an Existence Result
• On a class of superlinear elliptic problems
• Invariant criteria for existence of solutions to second-order quasilinear elliptic equations
• A note on the solvability in for the equation −Δu = f(x, u, Du)