Singular limits for 4-dimensional semilinear elliptic problems with exponential nonlinearity
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In this article, the existence of singular limits for semilinear elliptic problems with exponential nonlinearity was proved using some nonlinear domain decomposition method, and the singular limits were proved for a class of problems with nonlinear domains.Abstract:
Using some nonlinear domain decomposition method, we prove the existence of singular limits for solution of semilinear elliptic problems with exponential nonlinearity.read more
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Stable solutions for the bilaplacian with exponential nonlinearity.
TL;DR: In this paper, it was shown that the problem of finding the largest possible value of a unit ball in a unit normal vector has a unique weak solution for any constant Dirichlet boundary condition.
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Stable solutions for the bilaplacian with exponential nonlinearity
TL;DR: The problem with general constant Dirichlet boundary conditions is considered and it is shown that for $\lambda=\lambda^*$ this problem possesses a unique weak solution $u^*$.
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Singular limits for the bi-laplacian operator with exponential nonlinearity in $\R^4$
TL;DR: In this article, the authors consider the problem of finding the singular cohomology group with coefficients in a bounded smooth domain in a given number of points in the Euclidean plane.
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Asymptotic behavior of a fourth order mean field equation with Dirichlet boundary condition
Frédéric Robert,Juncheng Wei +1 more
TL;DR: In this article, the authors considered asymptotic behavior of the following fourth order equation ∇ 2 u = ρ e u /∫ Ω e u d x in Ω, u= δv u = 0 on δΩ Δ 2 u, where Q is a smooth oriented bounded domain in Ρ 4.
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Singular limits for the bi-Laplacian operator with exponential nonlinearity in R4
TL;DR: In this paper, the authors consider a bounded smooth domain in R 4 such that for some integer d ⩾ 1 its d-th singular cohomology group with coefficients in some field is not zero.
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