Nodal solutions for an elliptic equation in an annulus without the signum condition
Bull. Korean Math. Soc. 2020 Vol. 57, No. 2, 331-343
https://doi.org/10.4134/BKMS.b190227
Published online August 20, 2019
Printed March 31, 2020
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.
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