Extremal solutions and strong relaxation for second order multivalued boundary value problems

Leszek Gasiński; Nikolaos S. Papageorgiou

Czechoslovak Mathematical Journal (2005)

  • Volume: 55, Issue: 4, page 827-844
  • ISSN: 0011-4642

Abstract

top
In this paper we study semilinear second order differential inclusions involving a multivalued maximal monotone operator. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, we obtain “extremal” solutions and we prove a strong relaxation theorem.

How to cite

top

Gasiński, Leszek, and Papageorgiou, Nikolaos S.. "Extremal solutions and strong relaxation for second order multivalued boundary value problems." Czechoslovak Mathematical Journal 55.4 (2005): 827-844. <http://eudml.org/doc/30992>.

@article{Gasiński2005,
abstract = {In this paper we study semilinear second order differential inclusions involving a multivalued maximal monotone operator. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, we obtain “extremal” solutions and we prove a strong relaxation theorem.},
author = {Gasiński, Leszek, Papageorgiou, Nikolaos S.},
journal = {Czechoslovak Mathematical Journal},
keywords = {maximal monotone operator; pseudomonotone operator; Hartman condition; convex and nonconvex problems; extremal solutions; strong relaxation; maximal monotone operator; pseudomonotone operator; Hartman condition; convex and nonconvex problems},
language = {eng},
number = {4},
pages = {827-844},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Extremal solutions and strong relaxation for second order multivalued boundary value problems},
url = {http://eudml.org/doc/30992},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Gasiński, Leszek
AU - Papageorgiou, Nikolaos S.
TI - Extremal solutions and strong relaxation for second order multivalued boundary value problems
JO - Czechoslovak Mathematical Journal
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 4
SP - 827
EP - 844
AB - In this paper we study semilinear second order differential inclusions involving a multivalued maximal monotone operator. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, we obtain “extremal” solutions and we prove a strong relaxation theorem.
LA - eng
KW - maximal monotone operator; pseudomonotone operator; Hartman condition; convex and nonconvex problems; extremal solutions; strong relaxation; maximal monotone operator; pseudomonotone operator; Hartman condition; convex and nonconvex problems
UR - http://eudml.org/doc/30992
ER -

References

top
  1. 10.1016/0362-546X(86)90091-X, Nonlin. Anal. 10 (1986), 1083–1103. (1986) MR0857742DOI10.1016/0362-546X(86)90091-X
  2. 10.1006/jmaa.1996.0066, J.  Math. Anal. Appl. 198 (1996), 35–48. (1996) MR1373525DOI10.1006/jmaa.1996.0066
  3. 10.1016/S0362-546X(98)00044-3, Nonlin. Anal. 37 (1999), 217–245. (1999) MR1689752DOI10.1016/S0362-546X(98)00044-3
  4. The Baire category method in existence problem for a class of multivalued equations with nonconvex right hand side, Funkcialaj Ekvacioj 28 (1985), 139–156. (1985) MR0816823
  5. 10.1016/0022-247X(91)90101-5, J.  Math. Anal. Appl. 157 (1991), 469–494. (1991) MR1112329DOI10.1016/0022-247X(91)90101-5
  6. On the density of extremal solutions of differential inclusions, Annales Polon. Math.  LVI (1992), 133–142. (1992) MR1159984
  7. 10.1016/0362-546X(93)90075-4, Nonlin. Anal. 20 (1993), 871–894. (1993) MR1214750DOI10.1016/0362-546X(93)90075-4
  8. 10.1016/0362-546X(94)90245-3, Nonlin. Anal. 23 (1994), 669–681. (1994) Zbl0813.34021MR1297285DOI10.1016/0362-546X(94)90245-3
  9. Nonlinear boundary value problems for differential inclusions y ' ' ∈ F ( t , y , y ' ) , Annales Polon. Math.  LIV (1991), 195–226. (1991) MR1114171
  10. Theoremes d’existence des solutions d’inclusion differentielles, In: NATO ASI Series, Section C,  472, Kluwer, Dordrecht, 1995, pp. 51–87. (1995) MR1368670
  11. Coincidence Degree and Nonlinear Differential Equations. Lecture Notes in Math.  568, Springer-Verlag, New York, 1977. (1977) MR0637067
  12. Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems, Chapman and Hall/CRC Press, Boca Raton, 2005. (2005) MR2092433
  13. Boundary value problems of a class of quasilinear ordinary differential equations, Diff. Integ. Eqns. 6 (1993), 705–719. (1993) Zbl0784.34018
  14. 10.1006/jdeq.1998.3439, J.  Differ. Equations 147 (1998), 123–154. (1998) MR1632661DOI10.1006/jdeq.1998.3439
  15. 10.1090/S0002-9947-1960-0124553-5, Trans. AMS 96 (1960), 493–509. (1960) Zbl0098.06101MR0124553DOI10.1090/S0002-9947-1960-0124553-5
  16. Ordinary Differential Equations, Willey, New York, 1964. (1964) Zbl0125.32102MR0171038
  17. Periodic solutions for nonconvex differential inclusions, Proc. AMS 127 (1999), 89–94. (1999) MR1451808
  18. On the existence of periodic solutions for nonconvex-valued differential inclusions in  ℝ N , Proc. AMS 123 (1995), 3043–3050. (1995) MR1301503
  19. Handbook of Multivalued Analysis. Volume  I: Theory, Kluwer, Dordrecht, 1997. (1997) MR1485775
  20. Handbook of Multivalued Analysis. Volume  II: Applications, Kluwer, Dordrecht, 2000. (2000) MR1741926
  21. 10.1006/jdeq.1996.0173, J.  Differ. Equations 132 (1996), 107–125. (1996) MR1418502DOI10.1006/jdeq.1996.0173
  22. Neumann problem for a class of quasilinear differential equations, Atti. Sem. Mat. Fisico Univ. di Modena 48 (2000), 163–177. (2000) MR1767378
  23. On the existence of periodic solutions for second order vector differential equations, J.  Differ. Equations 9 (1971), 67–85. (1971) Zbl0211.11801MR0277824
  24. 10.1007/BF00251378, Arch. Rational Mech. Anal. 45 (1972), 294–320. (1972) MR0338765DOI10.1007/BF00251378
  25. 10.1016/S0362-546X(00)85028-2, Nonlin. Anal. 40 (2000), 497–503. (2000) Zbl0959.34014MR1768905DOI10.1016/S0362-546X(00)85028-2

NotesEmbed ?

top

You must be logged in to post comments.