Existence of Time Periodic Solutions of New Classes of Nonlinear Problems
Pure and Applied Mathematics Journal
Volume 4, Issue 5, October 2015, Pages: 189-215
Received: Jul. 30, 2015; Accepted: Aug. 17, 2015; Published: Aug. 26, 2015
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Authors
Luisa Toscano, Dep. of Math. and Appl.”R. Caccioppoli”,Univ. of Naples “Federico II”, via Cintia, Monte S. Angelo, Italy
Speranza Toscano, Dep. of Civil Ing,. Second Univ. of Naples, fac. of Ing., Aversa (CE), Italy
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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.
Keywords
Time Periodic, Evolution PDEs, Nonstationarity, Weak Periodic Solutions
To cite this article
Luisa Toscano, Speranza Toscano, Existence of Time Periodic Solutions of New Classes of Nonlinear Problems, Pure and Applied Mathematics Journal. Vol. 4, No. 5, 2015, pp. 189-215. doi: 10.11648/j.pamj.20150405.11
References
[1]
R.A. Adams, Sobolev spaces, Academic Press (1975).
[2]
S.Agmon, The Lp approach to the Dirichlet problem.I.Ann.Sc.Norm.Sup.Pisa (1959), 405-448.
[3]
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.
[4]
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.
[5]
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
[6]
J.L.Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris (1969).
[7]
X.Liu, Y.Zhang, H.Shi, Existence of periodic solutions for a class of nonlinear difference equations,Qualitative theory of Dynamical Systems, vol 14,issue 1 (2015), pp.51-69.
[8]
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.
[9]
R.Ma, R.Chen, Z.He, Positive periodic solutions of second-order differential equations with weak singularities, Applied Mathematics. and Computation, vol 232(2014), pp.97-103.
[10]
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.
[11]
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.
[12]
L.Toscano, S.Toscano, On the solvability of a class of general systems of variational equations with nonmonotone operators: a new result. Applications to Dirichlet and Neumann nonlinear problems, preprint (2015).
[13]
S.I. Pohozaev, On periodic solutions to certain nonlinear hyperbolic equations, Dokl. Akad. Nauk SSSR.(1971), vol.198.No 6, pp.1274-1277.
[14]
S.I. Pohozaev, On the global fibering method in nonlinear variational problems, Proc.Steklov Inst.of Math, 219 (1997), 281-328.
[15]
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.
[16]
E.Zeidler, Nonlinear functional analysis and its applications, II/A, Springer-Verlag (1980).
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