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Infinitely many solutions for a class of systems of differential inclusions

Part of: Existence theories Equations and inequalities involving nonlinear operators

Published online by Cambridge University Press:  19 January 2011

Brigitte E. Breckner  and
Csaba Varga
Brigitte E. Breckner
Affiliation:
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 Mihail Kogălniceanu, 400084 Cluj-Napoca, Romania ([email protected]; [email protected])
Csaba Varga
Affiliation:
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 Mihail Kogălniceanu, 400084 Cluj-Napoca, Romania ([email protected]; [email protected])
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Abstract

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Using a non-smooth version (due to Marano and Motreanu) of a variational principle of Ricceri we prove the existence of infinitely many solutions for certain systems of differential inclusions with various types of boundary conditions.

Keywords

locally Lipschitz functiongeneralized directional derivativesystems of differential inclusionsSobolev spaces

MSC classification

Secondary: 47J20: Variational and other types of inequalities involving nonlinear operators (general) 49J52: Nonsmooth analysis
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 1 , February 2011 , pp. 9 - 23
Copyright
Copyright © Edinburgh Mathematical Society 2011

References

1.Clarke, F. H., Nonsmooth analysis (Wiley, New York, 1983).Google Scholar
2.Di Falco, A. G., Infinitely many solutions to the Neumann problem for quasilinear elliptic systems, Matematiche 58 (2003), 117–130.Google Scholar
3.Di Falco, A. G., Infinitely many solutions to the Dirichlet problem for quasilinear elliptic systems, Matematiche 60 (2005), 163–179.Google Scholar
4.Faraci, F. and Kristály, A., One-dimensional scalar field equations involving an oscillatory nonlinear term, Discrete Contin. Dynam. Syst. 18 (2007), 107–120.CrossRefGoogle Scholar
5.Gasinski, L. and Papageorgiu, N., Nonsmooth critical point theory and nonlinear boundary value problems (Chapman & Hall/CRC, Boca Baton, FL, 2005).Google Scholar
6.Jebelean, P., Infinitely many solutions for ordinary p-Laplacian systems with nonlinear boundary conditions, Commun. Pure Appl. Analysis 7 (2008), 267–275.CrossRefGoogle Scholar
7.Jebelean, P. and Moroşanu, Gh., Mountain pass type solutions for discontinuous perturbations of the vector p-Laplacian, Nonlin. Funct. Analysis Applic. 10 (2005), 591–611.Google Scholar
8.Jebelean, P. and Morosşanu, Gh., Ordinary p-Laplacian systems with nonlinear boundary conditions, J. Math. Analysis Applic. 313 (2006), 738–753.CrossRefGoogle Scholar
9.Kristály, A., Infinitely many solutions for a differential inclusion problem in ℝN, J. Diff. Eqns 220 (2006), 511–530.CrossRefGoogle Scholar
10.Manásevich, R. and Mawhin, J., Periodic solutions for nonlinear systems with p-Laplacian like operators, J. Diff. Eqns 145 (1998), 367–393.CrossRefGoogle Scholar
11.Manásevich, R. and Mawhin, J., Boundary value problems for nonlinear perturbations of vector p-Laplacian like operators, J. Korean Math. Soc. 37 (2000), 665–685.Google Scholar
12.Marano, S. A. and Motreanu, D., Infinitely many critical points of non-differentiable functions and applications to a Neumann-type problem involving the p-Laplacian, J. Diff. Eqns 182 (2002), 108–120.CrossRefGoogle Scholar
13.Marano, S. A. and Motreanu, D., On a three critical points theorem for non-differentiable functions and applications to nonlinear boundary value problems, Nonlin. Analysis 48 (2002), 37–52.CrossRefGoogle Scholar
14.Mawhin, J., Some boundary value problems for Hartman type perturbations of the ordinary vector p-Laplacian, Nonlin. Analysis 40 (2000), 497–503.CrossRefGoogle Scholar
15.Mawhin, J. and Willem, M., Critical point theory and Hamiltonian systems (Springer, 1989).CrossRefGoogle Scholar
16.Motreanu, D. and Panagiotopoulos, P. D., Minimax theorems and qualitative properties of the solutions of hemivariational inequalities, Nonconvex Optimization and Its Applications, Volume 29 (Kluwer, Dordrecht, 1998).Google Scholar
17.Ricceri, B., A general variational principle and some of its applications, J. Computat. Appl. Math. 113 (2000), 401–410.CrossRefGoogle Scholar
18.Ricceri, B., Infinitely many solutions of the Neumann problem for elliptic equations involving the p-Laplacian, Bull. Lond. Math. Soc. 33 (2001), 331–340.CrossRefGoogle Scholar
19.Szulkin, A., Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems, Annales Inst. H. Poincaré 3 (1986), 77–109.CrossRefGoogle Scholar