On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions

Wenjie Gao; Junyu Wang

Annales Polonici Mathematici (1995)

  • Volume: 62, Issue: 3, page 283-291
  • ISSN: 0066-2216

Abstract

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The periodic boundary value problem u''(t) = f(t,u(t),u'(t)) with u(0) = u(2π) and u'(0) = u'(2π) is studied using the generalized method of upper and lower solutions, where f is a Carathéodory function satisfying a Nagumo condition. The existence of solutions is obtained under suitable conditions on f. The results improve and generalize the work of M.-X. Wang et al. [5].

How to cite

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Wenjie Gao, and Junyu Wang. "On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions." Annales Polonici Mathematici 62.3 (1995): 283-291. <http://eudml.org/doc/262667>.

@article{WenjieGao1995,
abstract = {The periodic boundary value problem u''(t) = f(t,u(t),u'(t)) with u(0) = u(2π) and u'(0) = u'(2π) is studied using the generalized method of upper and lower solutions, where f is a Carathéodory function satisfying a Nagumo condition. The existence of solutions is obtained under suitable conditions on f. The results improve and generalize the work of M.-X. Wang et al. [5].},
author = {Wenjie Gao, Junyu Wang},
journal = {Annales Polonici Mathematici},
keywords = {two-point boundary value problems; upper and lower solutions; Nagumo condition; existence; Carathéodory functions; second order periodic boundary value problem; Schauder fixed point theorem; minimal and maximal solutions; monotone iterative technique},
language = {eng},
number = {3},
pages = {283-291},
title = {On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions},
url = {http://eudml.org/doc/262667},
volume = {62},
year = {1995},
}

TY - JOUR
AU - Wenjie Gao
AU - Junyu Wang
TI - On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions
JO - Annales Polonici Mathematici
PY - 1995
VL - 62
IS - 3
SP - 283
EP - 291
AB - The periodic boundary value problem u''(t) = f(t,u(t),u'(t)) with u(0) = u(2π) and u'(0) = u'(2π) is studied using the generalized method of upper and lower solutions, where f is a Carathéodory function satisfying a Nagumo condition. The existence of solutions is obtained under suitable conditions on f. The results improve and generalize the work of M.-X. Wang et al. [5].
LA - eng
KW - two-point boundary value problems; upper and lower solutions; Nagumo condition; existence; Carathéodory functions; second order periodic boundary value problem; Schauder fixed point theorem; minimal and maximal solutions; monotone iterative technique
UR - http://eudml.org/doc/262667
ER -

References

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  1. [1] A. Adje, Sur et sous-solutions généralisées et problèmes aux limites du second ordre, Bull. Soc. Math. Belgique Sér. B 42 (1990), 347-368. Zbl0724.34018
  2. [2] J. Bebernes, A simple alternative problem for finding periodic solutions of second order ordinary differential systems, Proc. Amer. Math. Soc. 42 (1974), 121-127. Zbl0286.34055
  3. [3] A. Cabada and J. J. Nieto, A generalization of the monotone iterative technique for nonlinear second-order periodic boundary value problems, J. Math. Anal. Appl. 151 (1990), 181-189. Zbl0719.34039
  4. [4] J. J. Nieto, Nonlinear second-order periodic boundary value problems with Carathéodory functions, Appl. Anal. 34 (1989), 111-128. Zbl0662.34022
  5. [5] M.-X. Wang, A. Cabada and J. J. Nieto, Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions, Ann. Polon. Math. 58 (1993), 221-235. Zbl0789.34027

Citations in EuDML Documents

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  1. Nikolaos C. Kourogenis, Nikolaos S. Papageorgiou, Periodic solutions for quasilinear vector differential equations with maximal monotone terms
  2. Daqing Jiang, Junyu Wang, A generalized periodic boundary value problem for the one-dimensional p-Laplacian
  3. Tiziana Cardinali, Nikolaos S. Papageorgiou, Raffaella Servadei, The Neumann problem for quasilinear differential equations
  4. Lingbin Kong, Daqing Jiang, Multiple positive solutions of a nonlinear fourth order periodic boundary value problem
  5. Nikolaos Halidias, Nikolaos S. Papageorgiou, Second order multivalued boundary value problems
  6. Irena Rachůnková, Upper and lower solutions satisfying the inverse inequality

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