Existence of nodal solutions for quasilinear elliptic problems in ℝN
Published online by Cambridge University Press: 24 August 2015
We prove the existence of one positive, one negative and one sign-changing solution of a p-Laplacian equation on ℝN with a p-superlinear subcritical term. Sign-changing solutions of quasilinear elliptic equations set on the whole of ℝN have scarcely been investigated in the literature. Our assumptions here are similar to those previously used by some authors in bounded domains, and our proof uses fairly elementary critical point theory, based on constraint minimization on the nodal Nehari set. The lack of compactness due to the unbounded domain is overcome by working in a suitable weighted Sobolev space.
- Research Article
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 5 , October 2015 , pp. 937 - 957
- Copyright © Royal Society of Edinburgh 2015