1. Positivity of solutions of elliptic equations with nonlocal terms
- Author
-
A. Barabanova and W. Allegretto
- Subjects
Nonlinear system ,Partial differential equation ,Distribution (number theory) ,General Mathematics ,Mathematical analysis ,Value (mathematics) ,Eigenvalues and eigenvectors ,Mathematics - Abstract
In this paper we study a nonlocal problem for a second-order partial differential equation which depends on a parametern. We prove the existence of critical values 0
such that for all≦ɳ≦and for all non-negative right-hand sides, our problem has nonnegative solutions. We obtain a formula forɳ0, the maximal possible value of, and find the exact value of ɳ for spherical ɳ. We also study the corresponding eigenvalue problem. At the end of the paper, we consider the application of our results to the nonlinear system describing the distribution of temperature and potential in a microsensor. - Published
- 1996