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A remark on the nodal regions of the solutions of some superlinear elliptic equations*

Published online by Cambridge University Press:  14 November 2011

Vieri Benci  and
Donato Fortunato
Vieri Benci
Affiliation:
Istituto di Matematiche Applicate, Università, 56100 Pisa, Italy
Donato Fortunato
Affiliation:
Dipartimento di Matematica, Università, 70125 Bari, Italy
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Synopsis

We study the problem

where Ω is a bounded domain in ℝn(N≧3), 2 <p ≦2N/N – 2, λ ∈R. We prove the existence of nontrivial solutions of (*) for which we can estimate the number of nodal regions dependent on the eigenvalues of −Δ less than λ.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 111 , Issue 1-2 , 1989 , pp. 123 - 128
Copyright
Copyright © Royal Society of Edinburgh 1989

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