ON A SUPERLINEAR SECOND ORDER ELLIPTIC PROBLEM AT RESONANCE

Ruyun Ma; Zhongzi Zhao; Mantang Ma

doi:10.11948/20210356

2022 Volume 12 Issue 4

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Ruyun Ma, Zhongzi Zhao, Mantang Ma. ON A SUPERLINEAR SECOND ORDER ELLIPTIC PROBLEM AT RESONANCE[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1558-1566. doi: 10.11948/20210356

Citation:

Ruyun Ma, Zhongzi Zhao, Mantang Ma. ON A SUPERLINEAR SECOND ORDER ELLIPTIC PROBLEM AT RESONANCE[J]. Journal of Applied Analysis & Computation, 2022, 12(4): 1558-1566. doi: 10.11948/20210356

ON A SUPERLINEAR SECOND ORDER ELLIPTIC PROBLEM AT RESONANCE

1.
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
2.
School of Mathematics and Statistics, Xidian University, Xi'an, 710071, China

Corresponding author: Email: mary@nwnu.edu.cn(R. Ma)
Fund Project: The authors were supported by National Natural Science Foundation of China(12061064)

Abstract

Abstract

We show the existence of solutions of the superlinear problem

$ \begin{equation*} \begin{aligned} &-\Delta u=\lambda_1 u +f(u^+)+h(x),&&{\rm{in}} \ \Omega,\\ &u=0, && {\rm{on}} \ \partial\Omega, \end{aligned} \end{equation*} $

where $ \Omega\subset \mathbb{R}^N $ be a bounded domain whose boundary is a $ C^{2, \alpha} $ manifold, $ f $ satisfies some superlinear growth conditions and $ h $ satisfies a one-sided Landesman-Lazer condition. A priori bounds for the solutions of the equation is obtained by using Hardy-Sobolev type inequalities. Existence of solutions is then obtained by using topological degree arguments.
- Elliptic equations /
- superlinear nonlinearity /
- a priori bounds /
- topological degree
MSC: 35A16, 35B45, 35B34

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References

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