Global Bifurcation of Positive Solutions of Asymptotically Linear Elliptic Problems

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...

Positive Solutions and Global Bifurcation of Strongly Coupled Elliptic Systems

In this article, we study the existence of positive solutions for the coupled elliptic system −∆u = λ(f(u, v) + h1(x)) in Ω, −∆v = λ(g(u, v) + h2(x)) in Ω, u = v = 0 on ∂Ω, under certain conditions on f, g and allowing h1, h2 to be singular. We also consider the system −∆u = λ(a(x)u+ b(x)v + f1(v) + f2(u)) in Ω, −∆v = λ(b(x)u+ c(x)v + g1(u) + g2(v)) in Ω, u = v = 0 on ∂Ω, and prove a Rabinowitz...

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...

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...

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