An Exact Multiplicity Result for a Class of Semilinear Equations

Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions

This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.

Structure of the solution set for a class of semilinear elliptic equations with asymptotic linear nonlinearity

We consider a semilinear elliptic equation with asymptotic linear nonlinearity applying bifurcation theory and spectral analysis. We obtain the exact multiplicity of the positive solutions and a very precise structure of the solution set, which improves the previous knowledge of the problem.

. A P ] 1 S ep 2 00 5 On the exact number of bifurcation branches from a multiple eigenvalue ∗

We study local bifurcation from an eigenvalue with multiplicity greater than one for a class of semilinear elliptic equations. We evaluate the exact number of bifurcation branches of non trivial solutions and we compute the Morse index of the solutions in those branches.

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Exact multiplicity of positive solutions for a class of singular semilinear equations

The exact multiplicity of positive solutions of the singular semilinear equation ∆u+λf(u) = 0 with Dirichlet boundary condition is studied. The nonlinearity f that tends to infinity at zero, it is the linear combination of the functions u−α and up with α, p > 0. The number λ is a positive parameter. The goal is to determine all possible bifurcation diagrams that can occur for different values o...