Upper and lower solutions satisfying the inverse inequality

Irena Rachůnková

Annales Polonici Mathematici (1997)

  • Volume: 65, Issue: 3, page 235-244
  • ISSN: 0066-2216

Abstract

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We consider multipoint and two-point BVPs for second order ordinary differential equations with a Carathéodory right hand side. We prove the existence of solutions provided there exist upper and lower solutions of the BVP and the upper solution is less than the lower one.

How to cite

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Irena Rachůnková. "Upper and lower solutions satisfying the inverse inequality." Annales Polonici Mathematici 65.3 (1997): 235-244. <http://eudml.org/doc/269990>.

@article{IrenaRachůnková1997,
abstract = {We consider multipoint and two-point BVPs for second order ordinary differential equations with a Carathéodory right hand side. We prove the existence of solutions provided there exist upper and lower solutions of the BVP and the upper solution is less than the lower one.},
author = {Irena Rachůnková},
journal = {Annales Polonici Mathematici},
keywords = {existence; multipoint and two-point BVP; upper and lower solutions; topological degree; multipoint; two-point BVPs; Carathéodory right hand side},
language = {eng},
number = {3},
pages = {235-244},
title = {Upper and lower solutions satisfying the inverse inequality},
url = {http://eudml.org/doc/269990},
volume = {65},
year = {1997},
}

TY - JOUR
AU - Irena Rachůnková
TI - Upper and lower solutions satisfying the inverse inequality
JO - Annales Polonici Mathematici
PY - 1997
VL - 65
IS - 3
SP - 235
EP - 244
AB - We consider multipoint and two-point BVPs for second order ordinary differential equations with a Carathéodory right hand side. We prove the existence of solutions provided there exist upper and lower solutions of the BVP and the upper solution is less than the lower one.
LA - eng
KW - existence; multipoint and two-point BVP; upper and lower solutions; topological degree; multipoint; two-point BVPs; Carathéodory right hand side
UR - http://eudml.org/doc/269990
ER -

References

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  9. [9] J. Mawhin and J. R. Ward Jr. Periodic solutions of some forced Liénard differential equations at resonance, Arch. Math. (Basel) 41 (1983), 337-351. Zbl0537.34037
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  12. [12] I. Rachůnková, The first kind periodic solutions of differential equations of the second order, Math. Slovaca 39 (1989), 407-415. Zbl0753.34028
  13. [13] I. Rachůnková, An existence theorem of the Leray-Schauder type for four-point boundary value problems, Acta Univ. Palack. Olomuc. Fac. Rerum Nat. 100, Math. 30 (1991), 49-59. Zbl0752.34016
  14. [14] I. Rachůnková, On a transmission problem, Acta Univ. Palack. Olomuc. Fac. Rerum Nat. 105, Math. 31 (1992), 45-59. Zbl0807.34018
  15. [15] I. Rachůnková, On resonance problems for the second order differential equations, preprint. 
  16. [16] R. Reissig, Schwingungssätze für die verallgemeinerte Liénardsche Differentialgleichung, Abh. Math. Sem. Univ. Hamburg 44 (1975), 45-51. Zbl0323.34033
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