Linear and semilikear eigenvalue problems in Rn
- 1 January 1993
- journal article
- research article
- Published by Taylor & Francis in Communications in Partial Differential Equations
- Vol. 18 (1-2) , 215-240
- https://doi.org/10.1080/03605309308820928
Abstract
We consider the problem for , with respect to the existence and asymptotic behavior of solutions as For the linear, radially symmetric problem with , the number of zeros and asymptotic behavior of the solutions is known as λ> 0 varies. In this paper we study the linear equation as well as bounded and sublinear perturbations of the linear equation. For the nonsyrnmetric, linear and semilinear equations we investigate the structure of the set of X for which the solutions are positive and decay to zero. Unlike the symmetric linear case, these results cannot be derived directly from the fundamental structure theorem for linear ordinary differential equations. We work with topological methods and comparison theorems.This publication has 3 references indexed in Scilit:
- Entire solutions of singular elliptic equationsJournal of Mathematical Analysis and Applications, 1989
- On Quasisimilarity for Analytic Toeplitz OperatorsCanadian Mathematical Bulletin, 1988
- Nonlinear scalar field equations, I existence of a ground stateArchive for Rational Mechanics and Analysis, 1983