A non-smooth three critical points theorem with applications in differential inclusions

Journal of Global Optimization

Volumn 46, Issue 1, 2010, Pages 49-62

  Kristály, Alexandru ^a   Marzantowicz, Waclaw ^b   Varga, Csaba ^a  

^a BABE BOLYAI UNIVERSITY   (Romania)

^b ADAM MICKIEWICZ UNIVERSITY   (Poland)

Author keywords

Critical points; Differential inclusions; Locally Lipschitz functions

Indexed keywords

CRITICAL POINTS; CRITICAL POINTS THEOREM; DIFFERENTIAL INCLUSIONS; ELLIPTIC INCLUSIONS; LOCALLY LIPSCHITZ FUNCTION; NEUMANN BOUNDARY VALUE PROBLEMS; NON-HOMOGENEOUS; NON-SMOOTH; QUASI-LINEAR;

DIFFERENTIAL EQUATIONS; EQUATIONS OF STATE;

INCLUSIONS;

EID: 72449127177     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-009-9408-0     Document Type: Article

References (18)

1. D. Arcoya J. Carmona 2007 A nondifferentiable extension of a theorem of Pucci-Serrin and applications J. Differ. Equ. 235 2 683 700 10.1016/j.jde.2006. 11.022
2. G. Bonanno 2003 Some remarks on a three critical points theorem Nonlinear Anal. 54 651 665 10.1016/S0362-546X(03)00092-0
3. G. Bonanno 2004 A critical points theorem and nonlinear differential problems J. Global Optim. 28 3-4 249 258 10.1023/B:JOGO.0000026447.51988.f6
4. G. Bonanno P. Candito 2008 Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearity J. Differ. Equ. 244 12 3031 3059 10.1016/j.jde.2008.02.025
5. Brézis H.: Analyse Fonctionnelle-Théorie et Applications. Masson, Paris (1992)
6. K.C. Chang 1981 Variational methods for non-differentiable functionals and their applications to partial differential equations.J. Math Anal. Appl. 80 102 129 10.1016/0022-247X(81)90095-0
7. Clarke F.: Optimization and Nonsmooth Analysis. Wiley, New York (1983)
8. W. Krawcewicz W. Marzantowicz 1990 Some remarks on the Lusternik-Schnirelman method for non- differentiable functionals invariant with respect to a finite group action Rocky Mt. J. Math. 20 1041 1049 10.1216/rmjm/1181073061
9. N. J. Differ. Equ. 220 511 530 10.1016/j.jde.2005.02.007 (Pubitemid 41794222)
10. S.A. Marano D. Motreanu 2002 On a three critical points theorem for non-differentiable functions and applications to nonlinear boundary value problems Nonlinear Anal. 48 37 52 10.1016/S0362-546X(00)00171-1 (Pubitemid 33039256)
11. S.A. Marano N.S. Papageorgiou 2006 On a Neumann problem with p-Laplacian and non-smooth potential Differ. Integral Equ. 19 11 1301 1320
12. D. Motreanu Cs. Varga 1997 Some critical point results for locally Lipschitz functionals Comm. Appl. Nonlinear Anal. 4 17 33
13. P. Pucci J. Serrin 1985 A mountain pass theorem J. Differ. Equ. 60 142 149 10.1016/0022-0396(85)90125-1
14. B. Ricceri 2000 On a three critical points theorem Arch. Math. (Basel) 75 220 226
15. B. Ricceri 2000 Existence of three solutions for a class of elliptic eigenvalue problems Math. Comput. Model. 32 1485 1494 10.1016/S0895-7177(00) 00220-X (Pubitemid 30813552)
16. B. Ricceri 2002 Three solutions for a Neumann problem Topol. Methods Nonlinear Anal. 20 275 282
17. Ricceri, B.: A three critical points theorem revisited. Nonlinear Anal. doi: 10.1016/j.na.2008.04.010.
18. B. Ricceri 2006 Minimax theorems for limits of parametrized functions having at most one local minimum lying in a certain set Topol. Appl. 153 3308 3312 10.1016/j.topol.2005.06.020 (Pubitemid 44426389)