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A nonlinear elliptic problem with terms concentrating in the boundary
Semilinear elliptic equations nonlinear boundary conditions singular elliptic equations upper semicontinuity concentrating terms
2012/4/17
In this paper we investigate the behavior of a family of steady state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a $\epsilon$-neigh...
An elliptic problem with two singularities
elliptic problem two singularities Analysis of PDEs
2011/8/26
Abstract: We study a Dirichlet problem for an elliptic equation defined by a degenerate coercive operator and a singular right-hand side. We will show that the right-hand side has some regularizing ef...
A nonlinear degenerate elliptic problem with W^{1,1}_0 solutions
nonlinear degenerate elliptic problem Analysis of PDEs
2011/8/26
Abstract: We study a nonlinear equation with an elliptic operator having degenerate coercivity. We prove the existence of a unique W^{1,1}_0 distributional solution under suitable summability assumpti...
On the number of nodal solutions for a nonlinear elliptic problem on symmetric Riemannian manifolds
RiemannianManifolds Nodal Solutions Topological Meth-ods
2011/2/28
We consider the problem −"2gu+u = |u|p−2u in M, where (M, g) is a symmetric Riemannian manifold. We give a multiplicity result for antisymmetric changing sign solutions.
On the Existence of the Fundamental Eigenvalue of an Elliptic Problem in R^N
nonlinear eigenvalue problem nonlinear Schr¨odinger equation orbital stability
2011/2/28
We study an eigenvalue problem for functions in RN and we find sufficient conditions for the existence of the fundamental eigenvalue. This result can be applied to the study of the orbital stability o...
Properties of the extremal solution for a fourth-order elliptic problem
Properties extremal solution fourth-order elliptic problem
2010/12/6
Let ∗ > 0 denote the largest possible value of such that 2u = λ (1−u)p in B,0 < u ≤ 1 in B,u = ∂u ∂n = 0 on @B.has a solution, where B is the unit ball in Rn centered at th...