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We prove pointwise gradient bounds for entire solutions of pde’s of the form ℒu(x) = ψ(x, u(x), ∇u(x)), where ℒ is an elliptic operator (possibly singular or degenerate). Thus, we obtain some Liouville type rigidity results. Some classical results of J. Serrin are also recovered as particular cases of our approach.

Positive bound states having prescribed symmetry for a class of nonlinear elliptic equations in RN

Florin Catrina, Zhi-Qiang Wang (2001)

Annales de l'I.H.P. Analyse non linéaire

Positive Entire Solutions of Semilinear Elliptic Equations.

Nobuyoshi Fukagai (1986)

Mathematische Annalen

Positive radial solutions of nonlinear elliptic systems.

Ahammou, Abdelaziz (2001)

The New York Journal of Mathematics [electronic only]

Positive solutions for a class of quasilinear singular equations.

Goncalves, Jose Valdo, Santos, Carlos Alberto P. (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Positive solutions for concave-convex elliptic problems involving $p (x)$ -Laplacian

Makkia Dammak, Abir Amor Ben Ali, Said Taarabti (2022)

Mathematica Bohemica

We study the existence and nonexistence of positive solutions of the nonlinear equation $- Δ_{p (x)} u = λ k (x) u^{q} \pm h (x) u^{r} in Ω, u = 0 on \partial Ω$ where $Ω \subset ℝ^{N}$ , $N \geq 2$ , is a regular bounded open domain in $ℝ^{N}$ and the $p (x)$ -Laplacian $Δ_{p (x)} u : = {div (| \nabla u |}^{p (x) - 2} \nabla u)$ is introduced for a continuous function $p (x) > 1$ defined on $Ω$ . The positive parameter $λ$ induces the bifurcation phenomena. The study of the equation (Q) needs generalized Lebesgue and Sobolev spaces. In this paper, under suitable assumptions, we show that some variational methods still work. We use them to prove the existence of positive solutions...

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Picone-type inequalities for nonlinear elliptic equations and their applications.

Picone-type inequalities for nonlinear elliptic equations with first-order terms and their applications.

Plongements radiaux $S^{n} ↪ R^{n + 1}$ à courbure de Gauss positive prescrite

Points critiques dans les problèmes variationnels sans compacité

Pointwise curvature estimates for F-stable hypersurfaces

Pointwise estimates and rigidity results for entire solutions of nonlinear elliptic pde’s

Positive bound states having prescribed symmetry for a class of nonlinear elliptic equations in RN

Positive Entire Solutions of Semilinear Elliptic Equations.

Positive radial solutions of nonlinear elliptic systems.

Positive solutions for a class of quasilinear singular equations.

Positive solutions for concave-convex elliptic problems involving $p (x)$ -Laplacian

Positive solutions for elliptic equations with singular nonlinearity.

Positive solutions for elliptic problems with critical indefinite nonlinearity in bounded domains.

Positive solutions for indefinite inhomogeneous Neumann elliptic problems.

Positive solutions for nonlinear Schrödinger equations with deepening potential well

Positive solutions for semi-linear elliptic equations in exterior domains.

Positive Solutions of a Class of Second Order Semilinear Elliptic Equations in the Plane.

Positive solutions of an asymptotically planar system of elliptic boundary value problems.

Positive solutions of critical quasilinear elliptic problems in general domains.

Positive solutions of elliptic equations in two-dimensional exterior domains.

Currently displaying 21 – 40 of 58