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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Upper estimates for the energy of solutions of nonhomogeneous boundary value problems


Authors: Alfonso Castro and Mónica Clapp
Journal: Proc. Amer. Math. Soc. 134 (2006), 167-175
MSC (2000): Primary 35J20, 58E05; Secondary 34B15
Published electronically: August 11, 2005
MathSciNet review: 2170556
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Abstract: We establish upper bounds for the energy of critical levels of the functional associated to a perturbed superlinear elliptic boundary value problem. We show that the perturbed problem satisfies the estimates obtained by Bahri and Lions (1988) for the symmetric problem. We use these estimates to prove the existence of nonradial solutions to a radial elliptic boundary value problem. Our results fill a gap in an earlier paper by Aduén and Castro.


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Additional Information

Alfonso Castro
Affiliation: Department of Mathematics, Harvey Mudd College, Claremont, California 91711
Email: castro@math.hmc.edu

Mónica Clapp
Affiliation: Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, 04510 México, D.F., México
Email: mclapp@math.unam.mx

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08279-1
PII: S 0002-9939(05)08279-1
Keywords: Critical points, Morse index, nonradial solutions, semiclassical inequality, perturbed nonlinear elliptic equation
Received by editor(s): April 20, 2004
Published electronically: August 11, 2005
Additional Notes: This research was partially supported by PAPIIT, UNAM, México, under grant IN110902-3.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2005 American Mathematical Society