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Asymptotic boundary value problems for evolution inclusions


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.



  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)00365-7

    Article  MathSciNet  MATH  Google 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/S0002-9947-99-02297-7

    Article  MathSciNet  MATH  Google 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.

    Book  Google 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/S0308210500018291

    Article  MathSciNet  MATH  Google 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.

    MathSciNet  MATH  Google Scholar 

  10. Schaefer HH: Topological Vector Spaces. The Macmillan, New York; Collier-Macmillan, London; 1966:ix+294.

    MATH  Google Scholar 

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Correspondence to Tomáš Fürst.

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Fürst, T. Asymptotic boundary value problems for evolution inclusions. Bound Value Probl 2006, 68329 (2006).

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