Existence and Non-Existence Result for Singular Quasilinear Elliptic Equations

Existence Results for a Dirichlet Quasilinear Elliptic Problem

In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.

An existence result for a class of quasilinear singular competitive elliptic systems

In this paper we establish existence and regularity of positive solutions for a singular quasilinear elliptic system with competitive structure. The approach is based on comparison properties, a priori estimates and the Schauder’s …xed point theorem.

Existence of solutions for quasilinear degenerate elliptic equations ∗

In this paper, we study the existence of solutions for quasilinear degenerate elliptic equations of the form A(u) + g(x, u,∇u) = h, where A is a Leray-Lions operator from W 1,p 0 (Ω, w) to its dual. On the nonlinear term g(x, s, ξ), we assume growth conditions on ξ, not on s, and a sign condition on s.

Existence of Radial Solutions for Quasilinear Elliptic Equations with Singular Nonlinearities

We prove the existence of radial solutions of the quasilinear elliptic equation div(A(|Du|)Du) + f(u) = 0 in R, n > 1, where f is either negative or positive for small u > 0, possibly singular at u = 0, and growths subcritically for large u. Our proofs use only elementary arguments based on a variational identity. No differentiability assumptions are made on f .

Global Existence for Quasilinear Dispersive Equations