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Báo cáo hóa học: "RADIAL SOLUTIONS FOR A NONLOCAL BOUNDARY VALUE PROBLEM"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: RADIAL SOLUTIONS FOR A NONLOCAL BOUNDARY VALUE PROBLEM | RADIAL SOLUTIONS FOR A NONLOCAL BOUNDARY VALUE PROBLEM RICARDO ENGUIỌA AND LUÍS SANCHEZ Received 23 August 2005 Revised 20 December 2005 Accepted 22 December 2005 We consider the boundary value problem for the nonlinear Poisson equation with a nonlocal term - Au f u Jug u u du 0. We prove the existence of a positive radial solution when f grows linearly in u using Krasnoselskii s fixed point theorem together with eigenvalue theory. In presence of upper and lower solutions we consider monotone approximation to solutions. Copyright 2006 R. Enguica and L. Sanchez. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Let us consider the following nonlocal BVP in a ball u B 0 R of R -Au J u g u ju 1.1 u du 0 where f and g are continuous functions. For simplicity we shall take R 1. We want to study the existence of positive radial solutions u x v x 1.2 of 1.1 . This may be seen as the stationary problem corresponding to a class of nonlocal evolution parabolic boundary value problems related to relevant phenomena in engineering and physics. The literature dealing with such problems has been growing in the last decade. The reader may find some hints on the motivation for the study of this mathematical model for example in the paper by Bebernes and Lacey 1 . For more recent developments see 2 and the references therein. Hindawi Publishing Corporation Boundary Value Problems Volume 2006 Article ID 32950 Pages 1-18 DOI 10.1155 BVP 2006 32950 2 Radial solutions for a nonlocal boundary value problem Here we are considering a nonlocal term inserted in the right-hand side of the equation. Note however that it is also of interest to study boundary value problems where the nonlocal expression appears in a boundary condition. We refer the reader to the recent paper by Yang 13 and its references. When dealing .