PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Application of measures of weak noncompactness to a nonlocal Darboux problem

Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we study the existence of pseudosolutions of a nonlocal hyperbolic Darboux problem for the equation [...] with nonlocal boundary conditions u(x,0) + h1(x,u) = g1(x),u(0,y) + h2(y,u)=g2(y), on the bounded region. The functions considered have values in a Banach space and are weakly-weakly sequentially continuous, and the relevant integrals are Pettis integrals.
Wydawca
Rocznik
Strony
521--531
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
autor
  • Faculty of Mathematics and Computer Science Adam Mickiewicz University ul. Umultowska 87 61-614 Poznań, Poland, majcher@amu.edu.pl
Bibliografia
  • [1] J. M. Ball, Weak continuity properties of mappings and semi-groups, Proc. Roy. Soc. Edinburgh Sect. A 72(1979), 275-280.
  • [2] J. Banaś, K. Goebel, Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Applied Math. 60, Marcel Dekker Inc., New York, Basel, (1980).
  • [3] J. Banaś, J. Rivero, Measure of weak noncompactness, Ann. Mat. Pura Appl. 125 (1987), 213-224.
  • [4] L. Byszewski, Existence and uniqueness of mild and classical solutions of semilinear functional-differential evolution nonlocal Cauchy problem, Selected Problems of Mathematics, Cracow University of Technology, (1995).
  • [5] L. Byszewski, Existence and uniqueness of solutions of nonlocal problems for hyperbolic equation uxt = F(x, t, u, ux), J. Appl. Math. Stochastic Anal. 3 (1990), 163-168.
  • [6] L. Byszewski, Application of monotone iterative method to a system of parabolic semilinear functional-differential problems with nonlocal conditions, Nonlinear Analysis 28 (8), (1997), 1347-1357.
  • [7] L. Byszewski, N. S. Papageorgiou, An application of a noncompactness technique to an investigation of the existence of solutions to a nonlocal multivalued Darboux problem, J. Appl. Math. Stochastic Anal. 12 (1999), 179-190.
  • [8] L. Byszewski, A. Tabor, An application of the Kuratowski measure of noncompactness to an investigation of the existence of solutions of an abstract integrodifferential problem, Nonlinear Studies 6 (1999), 111-122.
  • [9] M. Cichoń, I. Kubiaczyk, Kneser-type theorem for the Darboux problem in Banach spaces, Comment. Math. Univ. Carolin. 42 (2001), 267-279.
  • [10] M. Cichoń, I. Kubiaczyk, Kneser’s theorem for strong, weak and pseudosolutions of ordinary differential equations in Banach space, Ann. Polon. Math. 62 (1) (1995), 13-21.
  • [11] M. Cichoń, P. Majcher, On semilinear nonlocal Cauchy problems, Atti Sem. Mat. Fis. Univ. Modena 49 (2001), 363-376.
  • [12] M. Cichoń, P. Majcher, On some solutions of nonlocal Cauchy problems, Comment. Math. 42 (2003), 187-199.
  • [13] F. S. De Blasi, On a property of the unit sphere in a Banach space, Bull. Math. Soc. Sci. Math. R. S. Roumanie 21 (1977), 259-262.
  • [14] D. Dulst, Characterizations of Banach Spaces not Containing l1, CWI Tract, Amsterdam, (1989).
  • [15] I. Kubiaczyk, On a fixed point theorem for weakly sequentially continuous mapping, Disc. Math.-Diff. Inclusions 15 (1995), 15-20.
  • [16] I. Kubiaczyk, On the existence of solutions of differential equations in Banach spaces, Bull. Polish Acad. Sci. Math. 33 (1985), 607-614.
  • [17] I. Kubiaczyk, Existence theorem for hyperbolic equation in Banach space, Funct. Approx. Comment. Math. 26 (1988), 207-215.
  • [18] P. Majcher, The nonlocal Darboux problem on the bounded region, Dynam. Systems Appl. 14, No. (3-4) (2005), 381-392.
  • [19] A. Michalak, On the Fubini theorem for the Pettis integral for bounded functions, Bull. Polish Acad. Sci. Math. 49 (1) (2001), 1-14.
  • [20] A. R. Mitchell, C. H. Smith, An existence theorem for weak solutions of differential equations in Banach spaces, Nonlinear Equations in Abstract Spaces, V. Lakshmikantham ed., (1978), 387-404.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA5-0025-0007
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.