Existence of solution for a class of biharmonic equations
| Autor: | Najib Tsouli, Omar Chakrone, Omar Darhouche, Mostafa Rahmani |
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| Jazyk: | English<br />Portuguese |
| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Boletim da Sociedade Paranaense de Matemática, Vol 32, Iss 1, Pp 99-108 (2014) |
| Druh dokumentu: | article |
| ISSN: | 0037-8712 2175-1188 |
| DOI: | 10.5269/bspm.v32i1.16178 |
| Popis: | 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 $F(x,s)=\int_{0}^{s}{f(x,t)dt}$. |
| Databáze: | Directory of Open Access Journals |
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