Solutions and multiple solutions for periodic p-Laplacian systems with a non-smooth potential

References

• Kyritsi , STh , Matzakos , N and Papageorgiou , NS . 2002 . Periodic problems for strongly nonlinear second-order differential inclusions . J. Diff. Eqns , 183 : 279 – 302 .
   Web of Science ®Google Scholar
• Manásevich , RF and Mawhin , J . 1998 . Periodic solutions for nonlinear systems with p-Laplacian-like operators . J. Diff. Eqns , 145 : 367 – 393 .
   Web of Science ®Google Scholar
• Mawhin , J . 2000 . Some boundary value problems for Hartman-type perturbations of the ordinary vector p-Laplacian . Nonlinear Anal. , 40 : 497 – 503 .
   Google Scholar
• Mawhin , J . 2001 . “ Nonlinear Analysis and Its Applications to Differential Equations (Lisbon 1998) ” . In Periodic solutions of systems with p-Laplacian-like operators , Vol. 43 of Progress in Nonlinear Differential Equations and Their Applications Edited by: Grossinho , MR . 37 – 63 . Boston, MA : Birkhäuser Verlag .
   Google Scholar
• Papageorgiou , EH and Papageorgiou , NS . 2004 . Existence of solutions and of multiple solutions for nonlinear nonsmooth periodic systems . Czechoslovak Math. J. , 54 : 347 – 371 .
   Google Scholar
• Papageorgiou , EH and Papageorgiou , NS . 2004 . Strongly nonlinear multivalued periodic problems with maximal monotone terms . Diff. Integral Eqns. , 17 : 443 – 480 .
   Google Scholar
• Papageorgiou , EH and Papageorgiou , NS . 2005 . Nonlinear boundary value problems involving the p-Laplacian and p-Laplacian-like operators . Z. Anal. Anwendungen , 24 : 691 – 708 .
   Google Scholar
• Dinca , G and Jebelean , P . 2008 . A priori estimates for the vector p-Laplacian with potential boundary conditions . Arch. Math. , 90 : 60 – 69 .
   Google Scholar
• Gasiński , L . 2007 . Multiplicity theorems for periodic systems with a p-Laplacian-like operator . Nonlinear Anal. , 67 : 2632 – 2641 .
   Google Scholar
• Jebelean , P and Morosanu , G . 2005 . Mountain pass type solutions for discontinuous perturbations of the vector p-Laplacian . Nonlinear Funct. Anal. Appl. , 10 : 591 – 611 .
   Google Scholar
• Pasca , D . 2007 . Periodic solutions of second-order differential inclusions systems with the p-Laplacian . J. Math. Anal. Appl. , 325 : 90 – 100 .
   Google Scholar
• Teng , KM and Wu , X . 2008 . Existence and subharmonicity of solutions for nonlinear nonsmooth periodic systems with a p-Laplacian . Nonlinear Anal. , 68 : 3742 – 3756 .
   Google Scholar
• Szulkin , A . 1986 . Minimax principles for lower semicontinuous functions and applications to nonlinear boundary Value Problems . Ann. Inst. H Poincaré Anal. Non Linéaire , 3 : 77 – 109 .
   Web of Science ®Google Scholar
• Gasiński , L and Papageorgiou , NS . 2005 . Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems , Boca Raton, FL : Chapman and Hall/ CRC Press .
   Google Scholar
• Clarke , FH . 1983 . Optimization and Nonsmooth Analysis , New York : Wiley .
   Google Scholar
• Corvellec , JN . 2001 . On the second deformation lemma . Topol. Methods Nonlinear Anal. , 17 : 55 – 66 .
   Google Scholar
• Chang , KC . 1993 . “ Infinite-Dimensional Morse Theory and Multiple Solution Problems ” . In Progress in Nonlinear Differential Equations and Their Applications , Vol. 6 , Boston, MA : Birkhäuser Verlag .
   Google Scholar
• Gasiński , L and Papageorgiou , NS . 2006 . Nonlinear Analysis , Boca Raton, FL : Chapman and Hall/CRC Press .
   Google Scholar
• Mawhin , J and Willem , M . 1989 . Critical Point Theory and Hamiltonian Systems . Applied Mathematical Sciences , 74 Springer-Verlag, New York
   Google Scholar