A note on a superlinear indefinite Neumann problem with multiple positive solutions

Exact multiplicity of positive solutions to a superlinear problem ∗

We generalize previous uniqueness results on a semilinear elliptic equation with zero Dirichlet boundary condition and superlinear, subcritical nonlinearity. Our proof is based on a bifurcation approach and a Pohozaev type integral identity, which greatly simplifies the previous arguments.

On Finding Multiple Solutions to a Singularly Perturbed Neumann Problem

In this paper, in order to numerically solve for multiple positive solutions to a singularly perturbed Neumann boundary value problem in mathematical biology and other applications, a local minimax method is modified with new local mesh refinement and other strategies. Algorithm convergence and other related properties are verified. Motivated by the numerical algorithm and convinced by the nume...

An existence results on positive solutions for a reaction-diffusion model with logistics growth and indefinite weight

In this paper, using sub-supersolution argument, we prove an existence result on positive solution for an ecological model under certain conditions. It also describes the dynamics of the fish population with natural predation and constant yield harvesting. The assumptions are that the ecosystem is spatially homogeneous and the herbivore density is a constant which are valid assumptions for mana...

Existence of Infinitely Many Nodal Solutions for a Superlinear Neumann Boundary Value Problem

On Neumann “superlinear” elliptic problems

In this paper we are going to show the existence of a nontrivial solution to the following model problem,