Solutions with interior bubble and boundary layer for an elliptic Neumann problem with critical nonlinearity
We study positive solutions of the equation... where n = 3, 4.5 and ∊ > 0 is small, with Neumann boundary condition in a unit ball B. We prove the existence of solutions with an interior bubble at the center and a boundary layer at the boundary ∂ B. To cite this article: J. Wei, S. Yan, C. R. Acad. Sci. Paris, Ser. I 343 (2006).
On the Lazer-McKenna Conjecture involving critical and super-critical exponents
We prove the Lazer-McKenna conjecture for an elliptic problem of Ambrosetti-Prodi type with critical and supercritical nonlinearities by constructing solutions concentrating on higher dimensional manifolds, under some partially symmetric assumption on the domain.
Solutions with Interior and Boundary Peaks for the Neumann Problem of an Elliptic System of FitzHugh-Nagumo Type
We study the existence of peak solutions for the Neumann problem of an elliptic system of FitzHugh-Nagumo type. The solutions we construct have arbitrary many peaks on the boundary and arbitrary many peaks inside the domain, and all the peaks of the solutions approach some local minimum points of the mean curvature function of the boundary.
The Lazer-McKenna conjecture for an elliptic problem with critical growth, part II
We consider an elliptic problem of Ambrosetti–Prodi type involving critical Sobolev exponent. We prove that this problem has solutions blowing up near the boundary of the domain.
Multipilicity of Asymmetric Solutions for Nonlinear Elliptic Problems
In this paper we study the existence of multiple asymmetric positive solutions for the following symmetric problem...
Interior peak solutions for an elliptic system of FitzHugh-Nagumo type
We consider the Dirichlet problem for an elliptic system of FitzHugh-Nagumo type. We prove that the problem has a solution with a sharp peak inside the domain.
Multipeak solutions for an elliptic system of Fitzhugh-Nagumo type
We consider the Dirichlet problem for an elliptic system of FitzHugh-Nagumo type. We prove that the problem has solutions with arbitrary many sharp peaks near the boundary but not on the boundary.
An Elliptic Problem Related to Planar Vortex Pairs
In this paper, we study the existence and limiting behavior of the mountain pass solutions of the elliptic problem —Δu = λf(u — q(x)) in Ω C ℝ²; u 0 on ∂Ω, where q is a positive harmonic function. We show that the 'vortex core' Aλ = {x ∈ Ω: uλ (x) > q(x)} of the solution uλ, shrinks to a global minimum point of q on the boundary ∂Ω as λ → + ∞. Furthermore, we show that for each strict local minimum x₀ point of q(x) on the boundary ∂Ω, there exists a solution uλ whose vortex core shrinks to this strict local minimum point x₀ as λ → +∞.
Period-parabolic Logistic Equation with Spatial and Temporal Degeneracies
A basic goal of theoretical ecology is to understand how the interactions of individual organizations with each other under a certain inhabiting environment determine the spatiotemporal structure of distribution of populations. The diffusive logistic equation, which describes the spatial and temporal distribution of the population density of a single species, is one of the fundamental reaction-diffusion equation models in population biology. In this thesis, we are concerned with the periodic logistic equation with homogeneous Neumann boundary conditions. The theory for this basic case forms the foundation for further investigation of multispecies problems. The thesis consists of four chapters.