Hostname: page-component-7479d7b7d-c9gpj Total loading time: 0 Render date: 2024-07-13T22:30:50.450Z Has data issue: false hasContentIssue false

Critical point theorems with relaxed boundary condition and applications

Published online by Cambridge University Press:  17 April 2009

Yihong Du
Affiliation:
Department of Mathematics, Statistics and Computing Science, University of New England, Armidale NSW 2351, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper is a sequel to a recent paper by the author in this journal. We prove some -variants of the min-max type critical point theorems with relaxed boundary condition and then apply the abstract results to a semilinear elliptic boundary value problem.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Bartolo, P., Benci, V. and Fortunate, P., ‘Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity’, Nonlinear Anal. 7 (1983), 9811012.CrossRefGoogle Scholar
[2]Benci, V. and Rabinowitz, P.H., ‘Critical point theorems for indefinite functionals’, Invent. Math 52 (1979), 241273.CrossRefGoogle Scholar
[3]Chang, K.C., Critical point theory and its applications (Shanhai Sci. and Tech. Press, 1986).Google Scholar
[4]Capozzi, A., Lupo, D. and Solimini, S., ‘On the existence of a non trivial solution to nonlinear problems at resonance’, Nonlinear Anal. 13 (1989), 151163.CrossRefGoogle Scholar
[5]Du, Y., ‘A deformation lemma and some critical point theorems’, Bull. Austral. Math. Soc. 43 (1991), 161168.CrossRefGoogle Scholar
[6]Ghoussoub, N., ‘A minimax principle with a relaxed boundary condition’, Proc. Amer. Math. Soc (to appear).Google Scholar
[7]Ghoussoub, N., ‘Location, multiplicity and Morse indices of min-max critical points’, (preprint).Google Scholar
[8]Ghoussoub, N. and Preiss, D., ‘A mountain pass principle for locating and classifying critical points’, A.I.H.P.-Analyse non lineaire 6 (1989), 321330.CrossRefGoogle Scholar
[9]Guo, D., Sun, J. and Qi, G., ‘Some extensions of the mountain pass lemma’, Differential Integral Equations 1 (1988), 351358.CrossRefGoogle Scholar
[10]Pucci, P. and Serrin, J., ‘Extensions of the mountain pass lemma’, J. Funct. Anal. 59 (1984), 185210.CrossRefGoogle Scholar
[11]Pucci, P. and Serrin, J., ‘A mountain pass lemma’, J. Differential Equations 60 (1985), 142149.CrossRefGoogle Scholar
[12]Rabinowitz, P.H., Minimal methods in critical point theory with applications to differential equations, CBMS Regional Conf. Ser. in Math 65 (Amer. Math. Soc., Providence, RI, 1986).CrossRefGoogle Scholar
[13]Rabinowitz, P.H., ‘Some minimax theorems and applications to nonlinear partial differential equations’, in Nonlinear Analysis, (Cesari, L., Kannan, R. and Weinberger, H.F., Editors) (Academic Press, New York, 1978), pp. 161177.Google Scholar
[14]Thews, K., ‘A reduction method for some nonlinear Dirichlet problems’, Nonlinear Anal. 3 (1979), 795813.CrossRefGoogle Scholar