On a Class of Asymptotically Linear Elliptic Problems in RN

Multiplicity of Solutions for a Class of Fourth-Order Elliptic Problems with Asymptotically Linear Term

Bifurcation Problem for Biharmonic Asymptotically Linear Elliptic Equations

In this paper, we investigate the existence of positive solutions for the ellipticequation $Delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $Omega$ of $R^{n}$, $ngeq2$, with Navier boundary conditions. We show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...

Eigenvalue Problems for a Quasilinear Elliptic Equation on Rn

where λ ∈ R. Next, we state the general hypotheses which will be assumed throughout the paper. (E) Assume that N , p satisfy the following relation N > p > 1. (G) g is a smooth function, at least C1,α(RN ) for some α∈ (0,1), such that g ∈ L∞(RN ) and g(x) > 0, on Ω+, with measure of Ω+, |Ω+| > 0. Also there exist R0 sufficiently large and k > 0 such that g(x) <−k, for all |x| > R0. Generally, p...

Multiple Solutions for Asymptotically Linear Resonant Elliptic Problems

In this paper we establish the existence of multiple solutions for the semilinear elliptic problem (1.1) −∆u = g(x, u) in Ω, u = 0 on ∂Ω, where Ω ⊂ RN is a bounded domain with smooth boundary ∂Ω, a function g: Ω×R→ R is of class C1 such that g(x, 0) = 0 and which is asymptotically linear at infinity. We considered both cases, resonant and nonresonant. We use critical groups to distinguish the c...

On an Asymptotically Linear Elliptic Dirichlet Problem

where Ω is a bounded domain in RN (N ≥ 1) with smooth boundary ∂Ω. The conditions imposed on f (x, t) are as follows: (f1) f ∈ C(Ω×R,R); f (x,0) = 0, for all x ∈Ω. (f2) lim|t|→0( f (x, t)/t) = μ, lim|t|→∞( f (x, t)/t) = uniformly in x ∈Ω. Since we assume (f2), problem (1.1) is called asymptotically linear at both zero and infinity. This kind of problems have captured great interest since the pi...