An existence and multiplicity result for a periodic boundary value problem

Boris Rudolf

Mathematica Bohemica (2008)

  • Volume: 133, Issue: 1, page 41-61
  • ISSN: 0862-7959

Abstract

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A periodic boundary value problem for nonlinear differential equation of the second order is studied. Nagumo condition is not assumed on a part of nonlinearity. Existence and multiplicity results are proved using the method of lower and upper solutions. Results are applied to the generalized Liénard oscillator.

How to cite

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Rudolf, Boris. "An existence and multiplicity result for a periodic boundary value problem." Mathematica Bohemica 133.1 (2008): 41-61. <http://eudml.org/doc/250514>.

@article{Rudolf2008,
abstract = {A periodic boundary value problem for nonlinear differential equation of the second order is studied. Nagumo condition is not assumed on a part of nonlinearity. Existence and multiplicity results are proved using the method of lower and upper solutions. Results are applied to the generalized Liénard oscillator.},
author = {Rudolf, Boris},
journal = {Mathematica Bohemica},
keywords = {periodic boundary value problem; multiplicity result; method of lower and upper solutions; Liénard oscillator; periodic boundary value problem; multiplicity result; method of lower and upper solutions; Liénard oscillator},
language = {eng},
number = {1},
pages = {41-61},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An existence and multiplicity result for a periodic boundary value problem},
url = {http://eudml.org/doc/250514},
volume = {133},
year = {2008},
}

TY - JOUR
AU - Rudolf, Boris
TI - An existence and multiplicity result for a periodic boundary value problem
JO - Mathematica Bohemica
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 133
IS - 1
SP - 41
EP - 61
AB - A periodic boundary value problem for nonlinear differential equation of the second order is studied. Nagumo condition is not assumed on a part of nonlinearity. Existence and multiplicity results are proved using the method of lower and upper solutions. Results are applied to the generalized Liénard oscillator.
LA - eng
KW - periodic boundary value problem; multiplicity result; method of lower and upper solutions; Liénard oscillator; periodic boundary value problem; multiplicity result; method of lower and upper solutions; Liénard oscillator
UR - http://eudml.org/doc/250514
ER -

References

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  1. 10.1007/BF02022967, Acta Math. Sci. Hung. 7 (1956), 71–94. (1956) MR0079154DOI10.1007/BF02022967
  2. 10.1112/blms/18.2.173, Bull. London Math. Soc. 18 (1986), 173–186. (1986) MR0818822DOI10.1112/blms/18.2.173
  3. 10.1007/BFb0089537, Lect. Notes Math. 568 Springer, Berlin, 1977. (1977) MR0637067DOI10.1007/BFb0089537
  4. 10.1016/0022-0396(91)90103-G, J. Differ. Equations 94 (1991), 67–82. (1991) MR1133541DOI10.1016/0022-0396(91)90103-G
  5. 10.12775/TMNA.1996.020, Topol. Methods Nonlinear Anal. 8 (1996), 25–56. (1996) MR1485756DOI10.12775/TMNA.1996.020
  6. Remarks on Nagumo’s condition, Portugaliae Mathematica 55 (1998), 1–9. (1998) Zbl0894.34015MR1612323
  7. 10.1016/0022-0396(72)90028-9, J. Differ. Equations 12 (1972), 610–636. (1972) Zbl0244.47049MR0328703DOI10.1016/0022-0396(72)90028-9
  8. Points fixes, points critiques et problèmes aux limites, Sémin. Math. Sup. no. 92, Presses Univ. Montréal, Montréal, 1985. (1985) Zbl0561.34001MR0789982
  9. 10.1016/0022-0396(84)90180-3, J. Differ. Equations 52 (1984), 264–287. (1984) MR0741271DOI10.1016/0022-0396(84)90180-3
  10. 10.1016/0022-247X(88)90383-6, J. Math. Anal. Appl. 130 (1988), 22–29. (1988) Zbl0678.34022MR0926825DOI10.1016/0022-247X(88)90383-6
  11. Non-ordered lower and upper solutions and solvability of the periodic problem for the Liénard and the Raleigh equations, Rend. Inst. Mat. Univ. Trieste 20 (1988), 54–64. (1988) 
  12. 10.1016/0362-546X(92)90016-8, Nonlinear Anal., Theory Methods Appl. 18 (1992), 497–505. (1992) DOI10.1016/0362-546X(92)90016-8
  13. 10.1016/0362-546X(94)90113-9, Nonlinear Anal., Theory Methods Appl. 22 (1994), 1315–1322. (1994) MR1280199DOI10.1016/0362-546X(94)90113-9
  14. 10.1006/jmaa.1999.6375, J. Math. Anal. Appl. 234 (1999), 311–327. (1999) DOI10.1006/jmaa.1999.6375
  15. 10.1016/0022-247X(90)90341-C, J. Math. Anal. Appl. 146 (1990), 203–206. (1990) MR1041210DOI10.1016/0022-247X(90)90341-C
  16. 10.1016/0362-546X(95)00144-K, Nonlinear Anal., Theory Methods Appl. 28 (1997), 137–144. (1997) Zbl0859.34016MR1416037DOI10.1016/0362-546X(95)00144-K
  17. Method of lower and upper solutions for a generalized boundary value problem, Archivum Mathematicum (Brno) 36 (2000), 595–602. (2000) Zbl1090.34520MR1822829
  18. Il problema dei valori ai limiti studiato il grande per gli integrali di una equazione differenziale del secondo ordine, Giorn. Mat. Battagliani, III. Ser. 69 (1931), 77–112. (1931) 
  19. On some nonlinear boundary value problems for ordinary differential equations, Archivum Mathematicum (Brno) 25 (1989), 207–222. (1989) MR1188065
  20. 10.2140/pjm.1996.172.255, Pacific J. Math. 172 (1996), 255–297. (1996) Zbl0862.34015MR1379297DOI10.2140/pjm.1996.172.255

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