On the existence of multiple solutions for a nonlocal BVP with vector-valued response

Andrzej Nowakowski; Aleksandra Orpel

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 2, page 621-640
  • ISSN: 0011-4642

Abstract

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The existence of positive solutions for a nonlocal boundary-value problem with vector-valued response is investigated. We develop duality and variational principles for this problem. Our variational approach enables us to approximate solutions and give a measure of a duality gap between the primal and dual functional for minimizing sequences.

How to cite

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Nowakowski, Andrzej, and Orpel, Aleksandra. "On the existence of multiple solutions for a nonlocal BVP with vector-valued response." Czechoslovak Mathematical Journal 56.2 (2006): 621-640. <http://eudml.org/doc/31054>.

@article{Nowakowski2006,
abstract = {The existence of positive solutions for a nonlocal boundary-value problem with vector-valued response is investigated. We develop duality and variational principles for this problem. Our variational approach enables us to approximate solutions and give a measure of a duality gap between the primal and dual functional for minimizing sequences.},
author = {Nowakowski, Andrzej, Orpel, Aleksandra},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonlocal boundary-value problems; positive solutions; duality method; variational method; positive solutions; duality method; variational method},
language = {eng},
number = {2},
pages = {621-640},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the existence of multiple solutions for a nonlocal BVP with vector-valued response},
url = {http://eudml.org/doc/31054},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Nowakowski, Andrzej
AU - Orpel, Aleksandra
TI - On the existence of multiple solutions for a nonlocal BVP with vector-valued response
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 2
SP - 621
EP - 640
AB - The existence of positive solutions for a nonlocal boundary-value problem with vector-valued response is investigated. We develop duality and variational principles for this problem. Our variational approach enables us to approximate solutions and give a measure of a duality gap between the primal and dual functional for minimizing sequences.
LA - eng
KW - nonlocal boundary-value problems; positive solutions; duality method; variational method; positive solutions; duality method; variational method
UR - http://eudml.org/doc/31054
ER -

References

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  1. Existence results for superlinear semipositone BVP’s, Proc. A.M.S. 124 (1996), 757–763. (1996) MR1317029
  2. On the theory of nonlocal boundary value problems, Soviet Math. Dokl. 30 (1984), 8–10. (1984) Zbl0586.30036MR0757061
  3. Some elementary generalizations of linear elliptic boundary value problems, Dokl. Akad. Nauk SSSR 185 (1969), 739–740. (1969) MR0247271
  4. Multiplicity of positive solutions for a nonlinear differential equation with nonlinear boundary conditions, Annales Polonici Math. LXIX.2 (1998), 155–165. (1998) MR1641876
  5. Positive solutions and nonlinear multipoint conjugate eigenvalue problems, Electronic J. of Differential Equations 03 (1997), 1–11. (1997) MR1428301
  6. On the existence of positive solutions of ordinary differential equations, Proc. A.M.S. 120 (1994), 743–748. (1994) MR1204373
  7. 10.1016/0022-247X(92)90179-H, J. Math. Anal. Appl. 168 (1992), 540–551. (1992) Zbl0763.34009MR1176010DOI10.1016/0022-247X(92)90179-H
  8. 10.1016/0362-546X(94)90137-6, Nonlinear Analysis TMA 23 (1994), 1427–1436. (1994) MR1306681DOI10.1016/0362-546X(94)90137-6
  9. Solvability of a generalized multipoint boundary value problem of mixed type for second order ordinary differential equations, Proc. Dynamic Systems and Applications 2 (1996), 215–222. (1996) MR1419531
  10. 10.1016/S0096-3003(97)81653-0, Appl. Math. Comput 89 (1998), 133–146. (1998) MR1491699DOI10.1016/S0096-3003(97)81653-0
  11. 10.1006/jmaa.1997.5334, J. Math. Anal. Appl. 208 (1997), 252–259. (1997) MR1440355DOI10.1006/jmaa.1997.5334
  12. Nonlocal boundary value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects, Differ. Equ. 23 (1987), 803–811. (1987) 
  13. Nonlocal boundary value problem of the second kind for a Sturm-Liouville operator in its differential and finite difference aspects, Differ. Equ. 23 (1987), 979–987. (1987) 
  14. Positive solutions of a boundary-value problem for second order ordinary differential equations, Electronic Journal of Differential Equations 49 (2000 2000), 1–9. (2000 2000) MR1772734
  15. Positive solutions for a nonlocal boundary-value problem with increasing response, Electronic Journal of Differential Equations 73 (2000), 1–8. (2000) MR1801638
  16. Multiple positive solutions for a nonlocal boundary-value problem with response function quiet at zero, Electronic Journal of Differential Equations 13 (2001), 1–10. (2001) MR1811786
  17. Existence of multiple solutions for a nonlocal boundary-value problem, Topol. Math. Nonl. Anal. 19 (2000), 109–121. (2000) MR1921888
  18. Positive solutions of operator equations, Noordhoff, Groningen, 1964. (1964) MR0181881
  19. Positive solutions for a nonlinear three-point boundary-value problem, Electronic Journal of Differential Equations 34 (1998), 1–8. (1998) 
  20. 10.1006/jmaa.2000.7320, J. Math. Anal. Appl. 256 (2001), 556–567. (2001) MR1821757DOI10.1006/jmaa.2000.7320
  21. Existence of positive solutions for second order m-point boundary value problems, Annales Polonici Mathematici LXXIX.3 (2002), 256–276. (2002) Zbl1055.34025MR1957802
  22. Problèmes de Dirichlet Variationnels Non Linéares, Les Presses de l’Université de Montréal (1987). (1987) MR0906453
  23. 10.1016/0022-0396(92)90089-6, J. Differential Eqns. 97 (1992), 174–188. (1992) Zbl0759.34039MR1161317DOI10.1016/0022-0396(92)90089-6
  24. Positive solutions for a nonlocal boundary-value problem with vector-valued response, Electronic J. of Differential Equations 46 (2002), 1–15. (2002) MR1907722
  25. Minimax Methods in Critical Points Theory with Applications to Differential Equations, AMS, Providence, 1986. (1986) MR0845785
  26. 10.1016/S0362-546X(01)00547-8, Nonlinear Anal. 47 (2001), 4319–4332. (2001) MR1975828DOI10.1016/S0362-546X(01)00547-8
  27. 10.1006/jdeq.1994.1042, J. Differential Equation 109 (1994), 1–4. (1994) MR1272398DOI10.1006/jdeq.1994.1042
  28. Minimax Theorems, Progress in Nonlinear Differential Equations and Their Applications. Basel, Boston, Berlin: Birkhäuser, Vol. 24, 1996. (1996) Zbl0856.49001MR1400007

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