The Nehari Manifold For A Quasilinear Elliptic Equation With Singular Weights And Nonlinear Boundary Conditions

Existences and Boundary Behavior of Boundary Blow-up Solutions to Quasilinear Elliptic Systems with Singular Weights

Using the method of explosive sub and supper solution, the existence and boundary behavior of positive boundary blow up solutions for some quasilinear elliptic systems with singular weight function are obtained under more extensive conditions.

A Fourth Order Elliptic Equation with Nonlinear Boundary Conditions

In this paper we study the existence of infinitely many nontrivial solutions of the following problem, −∆2u = u in Ω, − ∂∆u ∂ν = f(x, u) on ∂Ω, and either ∂u ∂ν = 0 or ∆u = 0 on ∂Ω. We assume that f(x, u) is superlinear and either subcritical or a sublinear perturbation of the critical case. For the proof in the critical case we apply the concentration compactness method.

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

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).

A Singular Quasilinear Anisotropic Elliptic Boundary Value Problem. Ii

Let Ω ⊂ RN with N ≥ 2. We consider the equations N ∑ i=1 ui ∂2u ∂xi + p(x) = 0, u|∂Ω = 0, with a1 ≥ a2 ≥ .... ≥ aN ≥ 0 and a1 > aN . We show that if Ω is a convex bounded region in RN , there exists at least one classical solution to this boundary value problem. If the region is not convex, we show the existence of a weak solution. Partial results for the existence of classical solutions for no...