Asymptotics of Solutions for Nonlocal Elliptic Problems in Plane Angles

Generalized Solutions of Nonlocal Elliptic Problems

An elliptic equation of order 2m with general nonlocal boundary-value conditions, in a plane bounded domain G with piecewise smooth boundary, is considered. Generalized solutions belonging to the Sobolev space Wm 2 (G) are studied. The Fredholm property of the unbounded operator corresponding to the elliptic equation, acting on L2(G), and defined for functions from the space Wm 2 (G) that satis...

Nonlocal Elliptic Boundary Value Problems

Asymptotics of Solutions for fully Nonlinear Elliptic Problems at Nearly Critical Growth

In this paper we deal with the study of limits of solutions of a class of fully nonlinear elliptic problems at nearly critical growth. By means of P.L. Lions’ concentrationcompactness principle, we prove an alternative result for the existence of non-trivial solutions of the limit problem.

Existence, Uniqueness and Multiplicity of Positive Solutions for Some Nonlocal Singular Elliptic Problems

In this article, using the sub-supersolution method and Rabinowitztype global bifurcation theory, we prove some results on existence, uniqueness and multiplicity of positive solutions for some singular nonlocal elliptic problems.

Positive solutions for a nonlinear nonlocal elliptic transmission problem

K e y w o r d s E l l i p t i c system, Transmission problem, Positive solution. 1. I N T R O D U C T I O N Let 12 be a smooth bounded domain of R n, n > 2, and let ~1 c gl be a subdomain with smooth boundary ~ satisfying ~1 C i2. Writing F = c9~ and gl2 = ~\~l l we have ~ = ~1 tJ 122 and 0i'~2 = ~, tJ F. We are concerned with the existence of positive solutions to the following system of nonli...