Global Solutions for Nonlinear Delay Evolution Inclusions with Nonlocal Initial Conditions
Tóm tắt
Từ khóa
Tài liệu tham khảo
Aizicovici, S., Lee, H.: Nonlinear nonlocal Cauchy problems in Banach spaces. Appl. Math. Lett. 18, 401–407 (2005)
Aizicovici, S., McKibben, M.: Existence results for a class of abstract nonlocal Cauchy problems. Nonlinear Anal. 39, 649–668 (2000)
Aizicovici, S., Papageorgiou, N.S., Staicu, V.: Periodic solutions of nonlinear evolution inclusions in Banach spaces. J. Nonlinear Convex. Anal. 7, 163–177 (2006)
Aizicovici, S., Pavel, N.H., Vrabie, I.I.: Anti-periodic solutions to strongly nonlinear evolution equations in Hilbert spaces. An. Ştiinţ. Univ. “Al. I. Cuza” Iaşi, Secţ. I a Mat. XLIV, 227–234 (1998)
Aizicovici, S., Staicu, V.: Multivalued evolution equations with nonlocal initial conditions in Banach spaces. Nonlinear Differ. Equ. Appl. (NoDEA) 14, 361–376 (2007)
Badii, M., Diaz, J.I., Tesei, A.: Existence and attractivity for a class of degenerate functional parabolic problems. Rend. Semin. Mat. Univ. Padova 78, 109–124 (1987)
Baras, P.: Compacité de l’opérateur definissant la solution d’une équation d’évolution non linéaire $(du/dt)+Au\ni f$ . C. R. Acad. Sci. Sér. I Math. 286, 1113–1116 (1978)
Barbu, V.: Nonlinear Semigroups and Differential Equation in Banach Spaces. Editura Academiei, Bucureşti, Noordhoff (1976)
Barbu, V.: Nonlinear Differential Equations of Monotone Type in Banach Spaces. Springer Monographs in Mathematics, Springer Verlag (2010)
Brezis, H., Strauss, W.: Semilinear elliptic equations in L 1. J. Math. Soc. Jpn. 25, 565–590 (1973)
Byszewski, L.: Theorems about the existence and uniqueness of solutions of semilinear evolution nonlocal Cauchy problems. J. Math. Anal. Appl. 162, 494–505 (1991)
Caşcaval, R., Vrabie, I.I.: Existence of periodic solutions for a class of nonlinear evolution equations. Rev. Mat. Univ. Complut. Madr. 7, 325–338 (1994)
Castaing, C., Monteiro-Marques, D.P.: Periodic solutions of evolution problems associated with a moving convex set. C. R. Acad. Sci. Paris, Série A 321, 531–536 (1995)
Cârjă, O., Necula, M., Vrabie, I.I.: Viability, Invariance and Applications. Elsevier Horth-Holland Mathematics Studies, vol. 207 (2007)
Deng, K.: Exponential decay of solutions of semilinear parabolic equations with initial boundary conditions. J. Math. Anal. Appl. 179, 630–637 (1993)
Diaz, J.I., Vrabie, I.I.: Existence for reaction diffusion systems: compactness method approach. J. Math. Anal. Appl. 188, 521–540 (1994)
Dunford, N., Schwartz, J.T.: Linear Operators Part I: General Theory. Interscience Publishers, Inc., New York (1958)
Edwards, R.E.: Functional Analysis. Rinehart and Winston, Holt (1965)
García-Falset, J.: Existence results and asymptotic behaviour for nonlocal abstract Cauchy problems. J. Math. Anal. Appl. 338, 639–652 (2008)
García-Falset, J., Reich, S.: Integral solutions to a class of nonlocal evolution equations. Commun. Contemp. Math. 12, 1032–1054 (2010)
Glicksberg, I.L.: A further genralization of the Kakutani fixed point theorem, with application to Nash equilibrium points. Proc. Am. Math. Soc. 3, 170–174 (1952)
Hale, J.: Theory of Functional Differential Equations. Springer Verlag, New York Heidelberg Belin (1977)
Hirano, N.: Existence of periodic solutions for nonlinear evolution equations in Hilbert spaces. Proc. Am. Math. Soc. 120, 185–192 (1994)
Hirano, N., Shioji, N.: Invariant sets for nonlinear evolution equations, Cauchy problems and periodic problems. Abstr. Appl. Anal. 3, 183–203 (2004)
Lakshmikantham, V., Leela, S.: Nonlinear Differential Equations in Abstract Spaces. International Series in Nonlinear Mathematics, vol. 2. Pergamon Press (1981)
Lakshmikantham, V., Papageorgiou, N.S.: Periodic solutions of nonlinear evolution inclusions. Comput. Appl. Math. 52, 277–286 (1994)
Li, Y.: Evolution equations with delays; time periodic solutions; asymptotic stability; analytic semigroups. J. Funct. Anal. 261, 1309–1324 (2011). doi: 10.1016/j.jfa.2011.05.001
Mitidieri, E., Vrabie, I.I.: Existence for nonlinear functional differential equations. Hiroshima Math. J. 17, 627–649 (1987)
Mitidieri, E., Vrabie, I.I.: A class of strongly nonlinear functional differential equations. Ann. Math. Pures Appl. CLI(IV), 125–147 (1988)
Paicu, A.: Periodic solutions for a class of differential inclusions in general Banach spaces. J. Math. Anal. Appl. 337, 1238–1248 (2008)
Paicu, A.: Periodic solutions for a class of nonlinear evolution equations in Banach spaces. An. Ştiinţ. “Al. I. Cuza”, Iaşi, Ser. Nouă Mat. LV, 107–118 (2009)
Paicu, A., Vrabie, I.I.: A class of nonlinear evolution equations subjected to nonlocal initial conditions. Nonlinear Anal. 72, 4091–4100 (2010)
Papageorgiou, N.S.: Periodic trajectories for evolution inclusions associated with time-dependent subdifferentials. Ann. Univ. Sci. Budapest 37, 139–155 (1994)
Hu, S., Papageorgiou, N.S.: On the existence of periodic solutions for a class of nonlinear inclusions. Bollettino UMI (7B), 591–605 (1993)
Vrabie, I.I.: Periodic solutions for nonlinear evolution equations in a Banach space. Proc. Am. Math. Soc. 109(3), 653–661 (1990)
Vrabie, I.I.: Compactness Methods for Nonlinear Evolutions. Pitman Monographs and Surveys in Pure and Applied Mathematics, 2nd edn., vol. 75. Longman and John Wiley & Sons (1995)
Vrabie, I.I.: Existence for nonlinear evolution inclusions with nonlocal retarded initial conditions. Nonlinear Anal. 74, 7047–7060 (2011)
Vrabie, I.I.: Nonlinear retarded evolution equations with nonlocal initial conditions. Dynamic Systems and Applications (in print)