Changmu Chu, Ying Yu, Multiplicity of positive radial solutions for semilinear elliptic equation with locally concave-convex variable exponent

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DOI: 10.23952/jnva.7.2023.1.03

Volume 7, Issue 1, 1 February 2023, Pages 35-47

Abstract. This paper is concerned with the following semilinear elliptic equation
$-\Delta u =u^{q(x)-1},$ in $B,$
$u>0,$ in $B,$
$u=0,$ in $\partial B,$
where $B$ is the unit ball in $\mathbb{R}^N(N\geq 3)$ , $q(x)=q(|x|)$ is a continuous radial function satifying $1\textless\min_{x \in \bar{B}}q(x)=q_-\textless 2\textless q_+=\max_{x \in \bar{B}}q(x)\textless 2^*=\frac{2N}{N-2}$ , and $q(0)>2$ . By means of variational methods and a priori estimate, we obtain that the problem above has at least two positive radial solutions.

How to Cite this Article:
C. Chu, Y. Yu, Multiplicity of positive radial solutions for semilinear elliptic equation with locally concave-convex variable exponent, J. Nonlinear Var. Anal. 7 (2023), 35-47.