Electron. J. Diff. Eqns., Vol. 2002(2002), No. 05, pp. 1-16.

Solutions to nonlinear elliptic equations with a nonlocal boundary condition

Yuandi Wang

We study an elliptic equation and its evolution problem on a bounded domain with nonlocal boundary conditions. Eigenvalue problems, existence, and dynamic behavior of solutions for linear and semilinear equations are investigated. We use the comparison principle and a semigroup approach.

Submitted June 15, 2001. Published January 8, 2002.
Math Subject Classifications: 35Q53, 42B35, 37K10, 35K55, 35K57.
Key Words: nonlocal boundary condition, eigenvalue, comparison principle, semigroup.

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Yuandi Wang
Department of Mathematics
Shanghai University
Shanghai 200436, China
e-mail: ydliwang@online.sh.cn

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