Multiple Positive Solutions of Semilinear Elliptic Problems in Exterior Domains

Multiple Positive Solutions of Semilinear Elliptic Problems in Exterior Domains

On the Existence of Multiple Positive Solutions for a Semilinear Problem in Exterior Domains

In this paper, we study the existence and nonexistence of multiple positive solutions for problem   ∆u+K(x)up = 0 in Ω. u > 0 in Ω, u ∈ H1 loc(Ω) ∩ C(Ω). u ∣∣ ∂Ω = 0, u → μ > 0 as |x| → ∞ where Ω = RN \ ω is an exterior domain in RN , ω ⊂ RN is a bounded domain with smooth boundary and N > 2. μ ≥ 0, p > 1 are some given constants. K(x) satisfies: K(x) ∈ Cα loc(Ω) and ∃C, ,M > 0 such t...

Existence of Positive Bounded Solutions of Semilinear Elliptic Problems

Correspondence should be addressed to Faten Toumi, [email protected] Received 18 June 2010; Accepted 25 September 2010 Academic Editor: A. Mikelic Copyright q 2010 Faten Toumi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Thi...

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 ...

Multiple Solutions For Semilinear Elliptic Boundary Value Problems At Resonance

In recent years several nonlinear techniques have been very successful in proving the existence of weak solutions for semilinear elliptic boundary value problems at resonance. One technique involves a variational approach where solutions are characterized as saddle points for a related functional. This argument requires that the Palais-Smale condition and some coercivity conditions are satisfie...