Constant Boundary value problem for a quasilinear elliptic system.
On the nonlinear Neumann problem at resonance with critical Sobolev nonlinearity
We consider the Neumann problem for the equation , u ∈ H¹(Ω), where Q is a positive and continuous coefficient on Ω̅ and λ is a parameter between two consecutive eigenvalues and . Applying a min-max principle based on topological linking we prove the existence of a solution.
A minimization problem associated with elliptic systems of Fitz–Hugh–Nagumo type
Peak solutions for an elliptic system of FitzHugh-Nagumo type
The aim of this paper is to study the existence of various types of peak solutions for an elliptic system of FitzHugh-Nagumo type. We prove that the system has a single peak solution, which concentrates near the boundary of the domain. Under some extra assumptions, we also construct multi-peak solutions with all the peaks near the boundary, and a single peak solution with its peak near an interior point of the domain.
Remarks on the Existence of Many Solutions of Certain Nonlinear Elliptic Equations
We show how a change of variable and peak solution methods can be used to prove that a number of nonlinear elliptic partial differential equations have many solutions.
Existence and uniqueness results on Single-Peaked solutions of a semilinear problem
The effect of the graph topology on the existence of multipeak solutions for nonlinear Schrödinger equations.
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