Advances in Differential Equations

Necessary and sufficient condition for existence and uniqueness of nodal solutions to sublinear elliptic equations

Ryuji Kajikiya

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Abstract

This paper deals with a sublinear elliptic equation $\Delta u + f(u)=0$ in a ball with the Dirichlet condition $u=0$ on the boundary. Under a suitable assumption on $f(\cdot)$, we establish the necessary and sufficient condition for the existence and uniqueness of radially symmetric nodal solutions.

Article information

Source
Adv. Differential Equations Volume 6, Number 11 (2001), 1317-1346.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1357139963

Mathematical Reviews number (MathSciNet)
MR1859350

Zentralblatt MATH identifier
1010.35040

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35J65: Nonlinear boundary value problems for linear elliptic equations

Citation

Kajikiya, Ryuji. Necessary and sufficient condition for existence and uniqueness of nodal solutions to sublinear elliptic equations. Adv. Differential Equations 6 (2001), no. 11, 1317--1346. https://projecteuclid.org/euclid.ade/1357139963.


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