Existence and nonexistence results for a weighted elliptic equation in exterior domains

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 and Nonexistence Results for Classes of Singular Elliptic Problem

and Applied Analysis 3 2. Proof of Theorems Consider the more general semilinear elliptic problem −Δu f x, u , in Ω, u > 0, in Ω, u 0, on ∂Ω, 2.1 where the function f x, s is locally Hölder continuous in Ω × 0,∞ and continuously differentiable with respect to the variable s. A function u is called to be a subsolution of problem 2.1 if u ∈ C2 Ω ∩ C Ω , and −Δu ≤ fx, u, in Ω, u > 0, in Ω, u 0, on...

Existence and Nonexistence Results for a Class of Quasilinear Elliptic Systems

Existence and bifurcation for some elliptic problems on exterior strip domains

We consider the semilinear elliptic problem −Δu + u = λK(x)up + f (x) in Ω, u > 0 in Ω, u ∈ H 0 (Ω), where λ ≥ 0, N ≥ 3, 1 < p < (N + 2)/(N − 2), and Ω is an exterior strip domain in RN . Under some suitable conditions on K(x) and f (x), we show that there exists a positive constant λ∗ such that the above semilinear elliptic problem has at least two solutions if λ∈ (0,λ∗), a unique positive sol...

Regularity and nonexistence results for anisotropic quasilinear elliptic equations in convex domains

For a class of anisotropic elliptic problems in bounded domains Ω we show that the convexity of Ω plays an important role in regularity and nonexistence results. Using recent results in [9] we improve some statements in [3]. 2000 Mathematical Subject Classification: 35J70, 46E35, 35B65.