A condition on the potential for the existence of doubly periodic solutions of a semi-linear fourth-order partial differential equation
We study the existence of solutions to the fourth order semi-linear equation $Delta ^2u=g(u)+h(x)$. We show that there is a positive constant $C_*$, such that if $g(xi )xi geq 0$ for $|xi |geq xi _0$ and $limsup _{|xi |o infty } 2G(xi )/xi^2<C_*$, then for all $hin L^2(Q)$ with $int _Q h dx=0$, t...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2000-10-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/conf-proc/05/c4/abstr.html |