## Differential and Integral Equations

### Multiplicity results for an inhomogeneous nonlinear elliptic problem

#### Abstract

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

#### Article information

Source
Differential Integral Equations, Volume 11, Number 1 (1998), 47-59.

Dates
First available in Project Euclid: 1 May 2013

https://projecteuclid.org/euclid.die/1367414133

Mathematical Reviews number (MathSciNet)
MR1607980

Zentralblatt MATH identifier
1042.35012

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc.

#### Citation

Noussair, Ezzat S.; Cao, Daomin. Multiplicity results for an inhomogeneous nonlinear elliptic problem. Differential Integral Equations 11 (1998), no. 1, 47--59. https://projecteuclid.org/euclid.die/1367414133