existence of solution for a class of biharmonic equations
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ID: 252265
2014
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Abstract
In this paper, We prove the solvability of the biharmonic problem
$$\begin{cases}\Delta^{2}u=f(x,u)+h ~~~~in~~\Omega, &\hbox{}\\
u=\Delta u=0 ~~~~~~on ~~\partial\Omega,\\\end{cases}$$
for a given function $h\in L^2(\Omega)$, if the limits at infinity of the quotients $f(x,s)/s$ and $2F(x,s)/s$ for a.e.$x\in\Omega$ lie between two consecutive eigenvalues of the biharmonic operator $\Delta^2$, where $F(x,s)$ denotes the primitive $F(x,s)=\int_{0}^{s}{f(x,t)dt}$.
| Reference Key |
tsouli2014boletimexistence
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|---|---|
| Authors | ;Najib Tsouli;Omar Chakrone;Omar Darhouche;Mostafa Rahmani |
| Journal | urban geography |
| Year | 2014 |
| DOI |
10.5269/bspm.v32i1.16178
|
| URL | |
| Keywords | Keywords not found |
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