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Non-zero solutions for a Schrödinger equation with indefinite linear and nonlinear terms

Published online by Cambridge University Press:  12 July 2007

David G. Costa ,
Hossein Tehrani  and
Miguel Ramos
David G. Costa
Affiliation:
Department of Mathematical Sciences, University of Nevada, Las Vegas, NV 89154-4020, USA (costa@unlv.nevada.edu)
Hossein Tehrani
Affiliation:
Department of Mathematical Sciences, University of Nevada, Las Vegas, NV 89154-4020, USA (tehranih@unlv.nevada.edu)
Miguel Ramos
Affiliation:
CMAF and Faculty of Sciences, University of Lisbon, Av. Prof. Gama Pinto, 1649-003 Lisboa, Portugal (mramos@ptmat.fc.ul.pt)
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Abstract

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We prove the existence of a non-trivial solution for the nonlinear elliptic problem −Δu + V(x)u = a(x)g(u) in RN, where g is superlinear near zero and near infinity, a(x) changes sign and V ∈ C(RN) is positive at infinity. For g odd, we prove the existence of an infinite number of solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 2 , April 2004 , pp. 249 - 258
Copyright
Copyright © Royal Society of Edinburgh 2004