Research Article Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains

Multiplicity of Positive and Nodal Solutions for Nonhomogeneous Elliptic Problems in Unbounded Cylinder Domains

Palais-smale Approaches to Semilinear Elliptic Equations in Unbounded Domains

Let Ω be a domain in RN , N ≥ 1, and 2∗ = ∞ if N = 1, 2, 2∗ = 2N N−2 if N > 2, 2 < p < 2 ∗. Consider the semilinear elliptic problem −∆u+ u = |u|p−2u in Ω; u ∈ H 0 (Ω). Let H1 0 (Ω) be the Sobolev space in Ω. The existence, the nonexistence, and the multiplicity of positive solutions are affected by the geometry and the topology of the domain Ω. The existence, the nonexistence, and the multipli...

Positive Solutions of Critical Quasilinear Elliptic Problems in General Domains

We consider a certain class of quasilinear elliptic equations with a term in the critical growth range. We prove the existence of positive solutions in bounded and unbounded domains. The proofs involve several generalizations of standard variational arguments.

Research Article Eigenvalue Problems and Bifurcation of Nonhomogeneous Semilinear Elliptic Equations in Exterior Strip Domains

We consider the following eigenvalue problems: −Δu+ u = λ( f (u) + h(x)) in Ω, u > 0 in Ω, u ∈H1 0 (Ω), where λ > 0, N =m+ n ≥ 2, n ≥ 1, 0 ∈ ω ⊆ Rm is a smooth bounded domain, S = ω×Rn, D is a smooth bounded domain in RN such that D ⊂⊂ S, Ω = S\ –– D. Under some suitable conditions on f and h, we show that there exists a positive constant λ∗ such that the above-mentioned problems have at least ...

A uniqueness and periodicity result for solutions of elliptic equations in unbounded domains

We proof a uniqueness and periodicity theorem for bounded solutions of uniformly elliptic equations in certain unbounded domains.