On an indefinite, non-Lipschitz semilinear elliptic problem: Compactly supported solutions, multiplicity and uniqueness

Uniqueness of Semilinear Elliptic Inverse Problem

We consider the uniqueness of the inverse problem for a semilinear elliptic differential equation with Dirichlet condition. The necessary and sufficient condition of a unique solution is obtained. We improved the results obtained by Isakov and Sylvester (1994) for the same problem.

Infinitely Many Solutions of Strongly Indefinite Semilinear Elliptic Systems

Existence and uniqueness of solutions for a semilinear elliptic system

We consider the existence, the nonexistence, and the uniqueness of solutions of some special systems of nonlinear elliptic equations with boundary conditions. In a particular case, the system reduces to the homogeneous Dirichlet problem for the biharmonic equation ∆ 2 u = |u| p in a ball with p > 0.

Existence and Uniqueness of Solutions to a Semilinear Elliptic System

In this article, we show the existence and uniqueness of smooth solutions for boundary-value problems of semilinear elliptic systems.

Multiplicity of Positive Solutions for Semilinear Elliptic Systems

and Applied Analysis 3 Let Kλ,μ : E → R be the functional defined by Kλ,μ (z) = ∫ Ω (λf (x) |u| q + μg (x) |V| q ) dx ∀z = (u, V) ∈ E. (11) We know that Iλ,μ is not bounded below on E. From the following lemma, we have that Iλ,μ is bounded from below on the Nehari manifoldNλ,μ defined in (9). Lemma 3. The energy functional Iλ,μ is coercive and bounded below onNλ,μ. Proof. If z = (u, V) ∈ Nλ,μ, ...