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1998 Multiplicity results for an inhomogeneous nonlinear elliptic problem
Daomin Cao, Ezzat S. Noussair
Differential Integral Equations 11(1): 47-59 (1998). DOI: 10.57262/die/1367414133


We are concerned with the multiplicity of positive and nodal solutions of $$ \begin{align} &-\Delta u +\mu u =Q(x) |u|^{p-2} u+h(x)\quad\text{in}\,\, \Omega\\ &\qquad\qquad u \in H_0^1(\Omega), \end{align} $$ where $N\geq 3$, $2<p<\frac{2N}{N-2}$ $\mu >0$, $Q\in C(\overline{\Omega})$, and $0\not\equiv h\in L^2(\Omega)$. We show that if the maximum of $Q$ is achieved at exactly $k$ different points of $\Omega$, then for large enough $\mu$ the above problem has at least $k+1$ positive solutions and $k$ no


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Daomin Cao. Ezzat S. Noussair. "Multiplicity results for an inhomogeneous nonlinear elliptic problem." Differential Integral Equations 11 (1) 47 - 59, 1998.


Published: 1998
First available in Project Euclid: 1 May 2013

zbMATH: 1042.35012
MathSciNet: MR1607980
Digital Object Identifier: 10.57262/die/1367414133

Primary: 35J60
Secondary: 35B05

Rights: Copyright © 1998 Khayyam Publishing, Inc.

Vol.11 • No. 1 • 1998
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