Abstract
We consider the variational system $-\Delta u = \lambda ( \nabla F)(u)$ in $\Omega$, $u = 0$ on $\partial \Omega$, where $\Omega$ is a bounded region in $\mathbb R^m$ ($m \geq 1$) with $C^1$ boundary, $\lambda$ is a positive parameter, $u\colon\Omega \rightarrow \mathbb R^N$ ($N > 1$), and $\Delta$ denotes the Laplace operator. Here $F\colon \mathbb R^N \rightarrow \R$ is a function of class $C^2$. Using variational methods, we show how changes in the sign of $F$ lead to multiple positive solutions.
Citation
Alfonso Castro. David Costa. Ratnasingham Shivaji. "Multiple positive solutions for a class of variational systems." Topol. Methods Nonlinear Anal. 50 (1) 1 - 8, 2017. https://doi.org/10.12775/TMNA.2017.016