Existence Results for Quasilinear Elliptic Equations with Indefinite Weight

Existence of Solutions for Quasilinear Elliptic Equations with Nonlinear Boundary Conditions and Indefinite Weight

In this article, we establish the existence and non-existence of solutions for quasilinear equations with nonlinear boundary conditions and indefinite weight. Our proofs are based on variational methods and their geometrical features. In addition, we prove that all the weak solutions are in C1,β(Ω) for some β ∈ (0, 1).

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.

Existence Results for Strongly Indefinite Elliptic Systems

In this paper, we show the existence of solutions for the strongly indefinite elliptic system −∆u = λu+ f(x, v) in Ω, −∆v = λv + g(x, u) in Ω, u = v = 0, on ∂Ω, where Ω is a bounded domain in RN (N ≥ 3) with smooth boundary, λk0 < λ < λk0+1, where λk is the kth eigenvalue of −∆ in Ω with zero Dirichlet boundary condition. Both cases when f, g being superlinear and asymptotically linear at infin...

Existence of ground state solutions for a class of nonlinear elliptic equations with fast increasing weight

‎This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight‎. ‎We apply the variational methods to prove the existence of ground state solution‎.

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations