Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2020; 57(2): 331-343

Online first article August 20, 2019      Printed March 31, 2020

https://doi.org/10.4134/BKMS.b190227

Copyright © The Korean Mathematical Society.

Nodal solutions for an elliptic equation in an annulus without the signum condition

Tianlan Chen, Yanqiong Lu, Ruyun Ma

Northwest Normal University; Northwest Normal University; Northwest Normal University

Abstract

This paper is concerned with the global behavior of components of radial nodal solutions of semilinear elliptic problems \[-\Delta v=\lambda h(x, v)\ \ \text{in}\ \Omega,\ \ \ v=0\ \ \text{on}\ \partial\Omega, \] where $\Omega=\{x\in \mathbb{R}^N: r_1<|x|0$ for $s\in\mathbb{R}\setminus\{0, s_1(x), s_2(x)\}$. Moreover, we give the intervals for the parameter $\lambda$ which ensure the existence and multiplicity of radial nodal solutions for the above problem. For this, we use global bifurcation techniques to prove our main results.

Keywords: Nodal solutions, elliptic equation, bifurcation

MSC numbers: Primary 34B15, 35J25

Supported by: This work was financially supported by NSFC No. 11801453, No. 11671322, and No. 11901464.