|
Two nontrivial solutions for quasilinear periodic equations
Author(s):
Evgenia
H.
Papageorgiou;
Nikolaos
S.
Papageorgiou
Journal:
Proc. Amer. Math. Soc.
132
(2004),
429-434.
MSC (2000):
Primary 34B15, 34C25
Posted:
June 17, 2003
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper we study a nonlinear periodic problem driven by the ordinary scalar p-Laplacian and with a Carathéodory nonlinearity. We establish the existence of at least two nontrivial solutions. Our approach is variational based on the smooth critical point theory and using the ``Second Deformation Theorem".
References:
- 1.
- R. Adams: Sobolev Spaces, Academic Press, New York (1975). MR 56:9247
- 2.
- P.Bartolo-V.Benci-D.Fortunato: Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity, Nonlinear Anal. 7 (1983), 981-1012. MR 85c:58028
- 3.
- K.-C. Chang: Infinite Dimensional Morse Theory and Multiple Solution Problems, Birkhäuser, Boston (1993). MR 94e:58023
- 4.
- H.Dang-S.F.Oppenheimer: Existence and uniqueness results for some nonlinear boundary value problems, J. Math. Anal. Appl. 198 (1996), 35-48. MR 96m:34033
- 5.
- M.Del Pino-R.Manasevich-A.Murua: Existence and multiplicity of solutions with prescribed period for a second order quasilinear ode, Nonlinear Anal. 18 (1992), 79-92. MR 92m:34055
- 6.
- C.Fabry-D.Fayyad: Periodic solutions of second order differential equations with a p-Laplacian and asymmetric nonlinearities, Rend. Istit. Mat. Univ. Trieste 24 (1992), 207-227. MR 96b:34027
- 7.
- Z. Guo: Boundary value problems of a class of quasilinear ordinary differential equations, Diff. Integral Eqns. 6 (1993), 705-719. MR 94d:34029
- 8.
- S.Hu-N.S.Papageorgiou: Handbook of Multivalued Analysis. Volume I: Theory, Kluwer, Dordrecht, The Netherlands (1997). MR 98k:47001
- 9.
- S.Kyritsi-N.Matzakos-N.S.Papageorgiou: Periodic problems for strongly nonlinear second order differential inclutions, J. Diff. Eqns. 183 (2002), 279-302.
- 10.
- R.Manasevich-J.Mawhin: Periodic solutions for nonlinear systems with p-Laplacian like operators, J. Diff. Eqns. 145 (1998), 367-393. MR 99c:34034
- 11.
- J. Mawhin: Periodic solutions of systems with
 -Laplacian-like operators in Nonlinear Analysis and Applications to Differential Equations, Lisbon (1997), Progress in Nonlinear Differential Equations and Applications, Birkhäuser, Boston (1998). MR 2002d:34029 - 12.
- J.Mawhin-M.Willem: Critical Point Theory and Hamiltonian Systems, Springer-Verlag, New York (1989). MR 90e:58016
- 13.
- M. Struwe: Variational Methods, Springer-Verlag, Berlin (1990). MR 92b:49002
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
34B15, 34C25
Retrieve articles in all Journals with MSC
(2000):
34B15, 34C25
Additional Information:
Evgenia
H.
Papageorgiou
Affiliation:
Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece
Nikolaos
S.
Papageorgiou
Affiliation:
Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece
Email:
npapg@math.ntua.gr
DOI:
10.1090/S0002-9939-03-07076-X
PII:
S 0002-9939(03)07076-X
Keywords:
Ordinary p-Laplacian,
critical point,
Palais-Smale condition,
second deformation theorem,
strong deformation retract,
strong resonance
Received by editor(s):
May 29, 2002
Received by editor(s) in revised form:
September 30, 2002
Posted:
June 17, 2003
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2003,
American Mathematical Society
|
Comments: webmaster@ams.org