A mountain pass theorem for a suitable class of functions

Rocky Mountain Journal of Mathematics

Volumn 39, Issue 3, 2009, Pages 707-727

  Averna, Diego ^a   Bonanno, Gabriele ^b  

^a UNIVERSITY OF PALERMO   (Italy)

^b UNIVERSITY MEDITERRANEA OF REGGIO CALABRIA   (Italy)

Author keywords

Critical points; Mountain pass; Palais Smale condition; Three solutions; Two point boundary value problem

Indexed keywords

EID: 69549103466     PISSN: 00357596     EISSN: None     Source Type: Journal    
DOI: 10.1216/RMJ-2009-39-3-707     Document Type: Article

References (22)

1. A. Ambrosetti and P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Functional Anal. 14 (1973), 349-381.
2. D. Averna and G. Bonanno, A three critical points theorem and its applications to the ordinary Dirichlet problem, Topol. Methods Nonlinear Anal. 22 (2003), 93-104.
3. -, Three solutions for a guasilinear two point boundary value problem involving the one-dimensional p-Laplacian, Proc. Edinburgh Math. Soc. 47 (2004), 257-270.
4. R.I. A very and J. Henderson, Three symmetric positive solutions for a second-order boundary value problem, Appl. Math. Letters 13 (2000), 1-7.
5. G. Bonanno, Multiple critical points theorems without the Palais-Smale condition, J. Math. Anal. Appl. 209 (2004), 600-614.
6. -, Some remarks on a three critical points theorem, Nonlinear Anal. 54 (2003), 651-665.
7. -, A critical points theorem and nonlinear differential problems, J. Global Optimization 28 (2004), 249-258.
8. G. Bonanno and P. Candito, Three solutions to a Neumann problem for elliptic equations involving the p-Laplacian, Arch. Math. 80 (2003), 424-429.
9. G. Bonanno and R. Livrea, Multiplicity theorems for the Dirichlet problem involving the p-Laplacian, Nonlinear Anal. 54 (2003), 1-7.
10. G. Bonanno and D. O'Regan, A boundary value problem on the half-line via critical point methods, Dynamic Syst. Appl. 15 (2006), 395-408.
11. K.-C. Chang, Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl. 80 (1981), 102-129.
12. F.H. Clarke, Optimization and nonsmooth analysis, Classics Appl. Math. 5, Soc. Indust. Appl. Mathematics, Philadelphia, 1990.
13. J. Henderson and H.B. Thompson, Existence of multiple solutions for second order boundary value problems, 3. Differential Equations 166 (2000), 443-454.
14. -, Multiple symmetric positive solutions for a second order boundary value problem, Proc. Amer. Math. Soc. 128 (2000), 2373-2379.
15. S.A. Marano and D. Motreanu, On a three critical points theorem for non differentiable functions and applications to non linear boundary value problems, Nonlinear Anal. 48 2002), 37-52.
16. D. Motreanu and V. Rǎdulescu, Variational and non-variational methods in nonlinear analysis and boundary value problems, Kluwer, Dordrecht, 2003.
17. P. Pucci and J. Serrin, A mountain pass theorem, 3. Differential Equations 63 (1985), 142-149.
18. P.H. Rabinowitz, Minimax methods in critical Point Theory with Applications to Differential Equations, CBMS Reg. Conf. Math. 65, American Mathematical Society, Providence, RI, 1986.
19. B. Ricceri, A general variational principle and some of its applications, J. Comput. Appl. Math. 113 (2000), 901-410.
20. -, On a three critical points theorem, Arch. Math. 75 (2000), 220-226.
21. R. Salvati, Multiple solutions for a mixed boundary value problem, Math. Sci. Res. J. 7 (2003), 275-983.
22. E. Zeidler, Nonlinear functional analysis and its applications, Vol.III., Springer-Verlag, Berlin, 1985.