Abstract
We consider the following nonlinear elliptic equation \begin{equation} \tag{0.1} A_\frac{1}{2} u = K(x) |u|^{p-1}u \hbox{ in } \Omega, \;\; u=0 \hbox{ on } \partial\Omega, \end{equation} where $\Omega$ is a bounded domain of $\mathbb{R}^n, n\geq 1, K(x)$ is a given function, $A_\frac{1}{2}$ represents the square root of $-\Delta$ in $\Omega$ with zero Dirichlet boundary condition and $1 < p < \frac{n+1}{n-1}$, $(p > 1$ if $n=1$). We apply the Brouwer's fixed point theorem to prove that (0.1) has infinitely many distinct solutions.
Citation
Khadijah Sharaf. "An infinite number of solutions for an elliptic problem with power nonlinearity." Differential Integral Equations 30 (1/2) 133 - 144, January/February 2017. https://doi.org/10.57262/die/1484881223