Nonradial solutions of a nonhomogeneous semilinear elliptic problem with linear growth

Nonradial Clustered Spike Solutions for Semilinear Elliptic Problems on S

We consider the following superlinear elliptic equation on S ε∆Snu− u + u = 0 in S, u > 0 in S where ∆Sn is the Laplace-Beltrami operator on S. We prove that for any k = 1, ..., n−1, there exists pk > 1 such that for 1 < p < pk and ε sufficiently small, there exist at least n − k positive solutions concentrating on k−dimensional subset of the equator. We also discuss the problem on geodesic bal...

Solutions of Semilinear Elliptic Equations with Asymptotic Linear Nonlinearity

In this paper, we consider some semilinear elliptic equations with asymptotic linear nonlinearity and show the existence, uniqueness, and asymptotic behavior of these solutions.

Multiple solutions and bifurcation of nonhomogeneous semilinear elliptic equations in R N ∗

Nodal Solutions for a Nonhomogeneous Elliptic Equation with Symmetry

We consider the semilinear problem −∆u + λu = |u|p−2u + f(u) in Ω, u = 0 on ∂Ω where Ω ⊂ RN is a bounded smooth domain, 2 < p < 2∗ = 2N/(N − 2) and f(t) behaves like tp−1−ε at infinity. We show that if Ω is invariant by a nontrivial orthogonal involution then, for λ > 0 sufficiently large, the equivariant topology of Ω is related with the number of solutions which change sign exactly once. The ...

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.