Open Access Open Access  Restricted Access Subscription or Fee Access

A New Approach for the Existence of Time Periodic Solutions of Special Classes of Nonlinear Problems


(*) Corresponding author


Authors' affiliations


DOI: https://doi.org/10.15866/iremos.v8i5.7869

Abstract


We study the existence of one or more weak periodic solutions of nonlinear evolution PDEs in a cylinder of RN+1 with conditions on lateral surface by using the results connected to a general evolution variational equation depending on a parameter. To this aim we state existence theorems and in some particular cases we give sufficient conditions about the nonstationarity of the found solutions. In these nonlinear evolution PDEs second partial derivatives with respect to time are also present.
Copyright © 2015 Praise Worthy Prize - All rights reserved.

Keywords


Weak Periodic; Evolution; Nonstationarity

Full Text:

PDF


References


S.I. Pohozaev, On periodic solutions to certain nonlinear hyperbolic equations, Dokl. Akad. Nauk SSSR.(1971), vol.198.No 6, pp.1274-1277.

S.I. Pohozaev, The existence and nonexistence of periodic solutions to certain nonlinear hyperbolic equations, Proceedings of the Steklov Institute of Mathematics, vol.227 (1999), pp.254-279.

C.Q.Dai, Y.Y.Wang, Notes on the equivalence of different variable separation approaches for nonlinear evolution equations, Communications in Nonlinear Science and Numerical Simulations, vol.19 (1) (2014),pp.19-28.
http://dx.doi.org/10.1016/j.cnsns.2013.05.027

J.Diblik, B.Iričanin, S.Stević, Note on the exixtence of periodic solutions of systems of differential-difference equations, Applied Mathematics. and Computation,vol 232(2014), pp. 922-928
http://dx.doi.org/10.1016/j.amc.2014.01.104

Z.Luo, Multiple positive periodic solutions for functional differential equations with impulses and a parameter, Abstract and Applied Analysis, vol 2014.
http://dx.doi.org/10.1155/2014/812867

http://dx.doi.org/10.1155/2014/812867.

E.Zeidler, Nonlinear functional analysis and its applications, II/A, Springer-Verlag (1980).
http://dx.doi.org/10.1007/978-1-4612-5020-3

L.Toscano, S.Toscano, On the solvability of a class of general systems of variational equations with nonmonotone operators, Journal of Interdisciplinary Mathematics 14, n.2, (2011), 123-147.
http://dx.doi.org/10.1080/09720502.2011.10700741

L.Toscano, S.Toscano, A new result concerning the solvability of a class of general systems of variational equations with nonmonotone operators. Applications to Dirichlet and Neumann nonlinear problems, in press on International Journal of Differential Equations (2015).

S.I. Pohozaev, On the global fibering method in nonlinear variational problems, Proc.Steklov Inst.of Math, 219 (1997), 281-328.

L.Toscano, S.Toscano, Dirichlet and Neumann problems related to nonlinear elliptic systems: solvability, multiple solutions, solutions with positive components, Abstract and Applied Analysis (2012), 1-44.
http://dx.doi.org/10.1155/2012/760854

R.A. Adams, Sobolev spaces, Academic Press (1975).

S.Agmon, The Lp approach to the Dirichlet problem. I.Ann.Sc.Norm.Sup.Pisa (1959), 405-448.

A.Anane, Simplicité et isolation de la première valeur propre du p-laplacian avec poids, C.R.Acad.Sci,Paris, Sér.I, 305 (1987), 725-728.

J.L.Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris (1969).
http://dx.doi.org/10.1007/bf02738151


Refbacks

  • There are currently no refbacks.


Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize