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A multiple linking minimax principle

Published online by Cambridge University Press:  17 April 2009

Dumitru Motreanu
Dumitru Motreanu
Affiliation:
Department of Mathematics, University of Iasi, 6600 Iasi, Romania
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The aim of this paper is three-fold: to fill the gap between different deformation lemmas, to obtain a unifying minimax result where multiple linking situations can occur, and to locate the critical points as solutions of minimisation problems.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 1 , February 1996 , pp. 39 - 49
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Ambrosetti, A. and Rabinowitz, P.H., ‘Dual variational methods in critical point theory and applications’, J. Funct. Anal. 14 (1973), 349–381.CrossRefGoogle Scholar
[2]Clark, D.C., ‘A variant of Lusternik-Schnirelman theory’, Indiana Univ. Math. J. 22 (1972), 65–74.CrossRefGoogle Scholar
[3]Ding, I., ‘A remark on the linking theorem with applications’, Nonlinear Anal. 22 (1994), 237–250.Google Scholar
[4]Du, Y., ‘A deformation lemma and some critical point theorems’ Bull. Austral. Math. Soc. 43 (1991), 161–168.CrossRefGoogle Scholar
[5]Ghoussoub, N. and Preiss, D., ‘A general mountain pass principle for locating classifying critical points’, Ann. Inst. H. Poincaré. Anal. Non Linéaire 6 (1989), 321–330.CrossRefGoogle Scholar
[6]Kavian, O., Introduction à la théorie des points critiques et applications aux problèmes elliptiques (Springer-Verlag, France, Paris, 1993).Google Scholar
[7]Motreanu, D., ‘Existence for minimization with nonconvex constraints’, J. Math. Anal. Appl. 117, 128–137.CrossRefGoogle Scholar
[8]Motreanu, D. and Naniewicz, Z., ‘Discontinuous semilinear problems in vector–valued function spaces’, Differential Integral Equations (to appear).Google Scholar
[9]Motreanu, D. and Panagiotopoulos, P.D., ‘Hysteresis: the eigenvalue problem for hemivariational inequalities’, in Models of Hysteresis, (Visintin, A., Editor) (Longman Scientific Technical, Harlow, 1993), pp. 102–117.Google Scholar
[10]Nirenberg, L., ‘Variational and topological methods in nonlinear problems’, Bull. Amer. Math. Soc. 4 (1981), 267–302.CrossRefGoogle Scholar
[11]Palais, R.S., ‘Lusternik-Schnirelman theory on Banach manifolds’, Topology 5 (1966), 115–132.CrossRefGoogle Scholar
[12]Panagiotopoulos, P.D., Hemivariational inequalities. Applications in mechanics and engineering (Springer-Verlag, Berlin, Heidelberg, New York, 1993).CrossRefGoogle Scholar
[13]Pucci, P. and Serrin, J., ‘Extensions of the mountain pass theorem’, J. Funct. Anal. 59 (1984), 185–210.CrossRefGoogle Scholar
[14]Rabinowitz, P.H., Minimax methods in critical point theory with applications to differential equations,CBMS Reg. Conf. Ser. Math. No. 65 (Amer. Math. Soc.,Providence, R.I.,1986).CrossRefGoogle Scholar
[15]Struwe, M., Variational methods. Applications to nonlinear partial differential equations and Hamiltonian systems (Springer-Verlag, Berlin, Heidelberg, New York, 1990).Google Scholar