Skip to content


  • Research Article
  • Open Access

Asymptotic boundary value problems for evolution inclusions

Boundary Value Problems20062006:68329

  • Received: 24 January 2005
  • Accepted: 17 July 2005
  • Published:


When solving boundary value problems on infinite intervals, it is possible to use continuation principles. Some of these principles take advantage of equipping the considered function spaces with topologies of uniform convergence on compact subintervals. This makes the representing solution operators compact (or condensing), but, on the other hand, spaces equipped with such topologies become more complicated. This paper shows interesting applications that use the strength of continuation principles and also presents a possible extension of such continuation principles to partial differential inclusions.


  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Function Space


Authors’ Affiliations

Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, Tomkova 40, Olomouc, 779 00, Czech Republic


  1. Andres J, Bader R: Asymptotic boundary value problems in Banach spaces. Journal of Mathematical Analysis and Applications 2002,274(1):437-457. 10.1016/S0022-247X(02)00365-7MathSciNetView ArticleMATHGoogle Scholar
  2. Andres J, Gabor G, Górniewicz L: Boundary value problems on infinite intervals. Transactions of the American Mathematical Society 1999,351(12):4861-4903. 10.1090/S0002-9947-99-02297-7MathSciNetView ArticleMATHGoogle Scholar
  3. Andres J, Górniewicz L: Topological Fixed Point Principles for Boundary Value Problems, Topological Fixed Point Theory and Its Applications. Volume 1. Kluwer Academic, Dordrecht; 2003:xvi+761.View ArticleGoogle Scholar
  4. Borsuk K: Theory of Retracts, Monografie Matematyczne. Volume 44. Państwowe Wydawnictwo Naukowe, Warsaw; 1967:251.Google Scholar
  5. Evans LC: Partial Differential Equations, Graduate Studies in Mathematics. Volume 19. American Mathematical Society, Rhode Island; 1998:xviii+662.Google Scholar
  6. Furi M, Pera MP: On the fixed point index in locally convex spaces. Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1987,106(1-2):161-168. 10.1017/S0308210500018291MathSciNetView ArticleMATHGoogle Scholar
  7. Gajewski H, Gröger K, Zacharias K: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Mathematische Lehrbücher und Monographien, II. Abteilung, Mathematische Monographien. Volume 38. Akademie, Berlin; 1974:ix+281.Google Scholar
  8. Hu S, Papageorgiou NS: Handbook of Multivalued Analysis. Vol. I. Theory, Mathematics and Its Applications. Volume 419. Kluwer Academic, Dordrecht; 1997:xvi+964.Google Scholar
  9. Margheri A, Zecca P: Solution sets and boundary value problems in Banach spaces. Topological Methods in Nonlinear Analysis 1993,2(1):179-188.MathSciNetMATHGoogle Scholar
  10. Schaefer HH: Topological Vector Spaces. The Macmillan, New York; Collier-Macmillan, London; 1966:ix+294.MATHGoogle Scholar


© Fürst 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.