Journal ArticleDOI
Boundary singularities of solutions of some nonlinear elliptic equations
Abdelilah Gmira,Laurent Veron +1 more
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This article is published in Duke Mathematical Journal.The article was published on 1991-11-01. It has received 158 citations till now. The article focuses on the topics: Boundary value problem & Quarter period.read more
Citations
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Spatial Branching Processes, Random Snakes and Partial Differential Equations
TL;DR: In this article, the authors present an overview of the history of continuous-state branching processes and superprocesses and their connections with statistical mechanics and interacting particle systems, including the connections with partial differential equations.
Book
Diffusions, Superdiffusions and Partial Differential Equations
TL;DR: In this article, the authors discuss the relationship between Markov processes and elliptic differential equations, including linear elliptic equations and diffusions, as well as branching exit Markov systems and superprocesses.
Journal ArticleDOI
The boundary trace of positive solutions of semilinear elliptic equations : The subcritical case
Moshe Marcus,Laurent Veron +1 more
Book ChapterDOI
Nonlinear problems related to the Thomas-Fermi equation
Philippe Bénilan,Haim Brezis +1 more
TL;DR: In this article, the porous medium equation (PME) was studied in terms of the Dirichlet condition, where 0 < p < ∞ and f ∈ L 1.
Journal ArticleDOI
Semilinear fractional elliptic equations involving measures
TL;DR: In this paper, the authors studied the existence and uniqueness of weak solutions to (E) ( − Δ ) α u + g ( u ) = ν in a bounded regular domain Ω in R N ( N ≥ 2 ) which vanish in R n ∖ Ω, where α denotes the fractional Laplacian with α ∈ ( 0, 1 ), ν is a Radon measure and g is a nondecreasing function satisfying some extra hypotheses.
References
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Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
Journal ArticleDOI
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
Book
Minimax methods in critical point theory with applications to differential equations
TL;DR: The mountain pass theorem and its application in Hamiltonian systems can be found in this paper, where the saddle point theorem is extended to the case of symmetric functionals with symmetries and index theorems.
Journal ArticleDOI
Bifurcation from simple eigenvalues
TL;DR: In this article, a general version of the main problem of bifurcation theory, given p ϵ C, determine the structure of G−1{0} in some neighborhood of p.