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1996-1997 | 65 | 3 | 235-244
Tytuł artykułu

Upper and lower solutions satisfying the inverse inequality

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
65
Numer
3
Strony
235-244
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-04-15
Twórcy
  • Department of Mathematics, Palacký University, Tomkova 40, 77900 Olomouc, Czech Republic
Bibliografia
  • [1] S. R. Bernfeld and V. Lakshmikantham, An Introduction to Nonlinear Boundary Value Problems, Academic Press, New York, 1974.
  • [2] E. N. Dancer, On the ranges of certain damped nonlinear differential equations, Ann. Mat. Pura Appl. (4) 119 (1979), 281-295.
  • [3] R. Gaines and J. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Lecture Notes in Math. 568, Springer, Berlin, 1977.
  • [4] W. Gao and J. Wang, On a nonlinear second order periodic boundary value problem with Carathéodory functions, Ann. Polon. Math. 62 (1995), 283-291.
  • [5] I. T. Kiguradze, Some Singular Boundary Value Problems for Ordinary Differential Equations, Univ. Press, Tbilisi, 1975 (in Russian).
  • [6] H. W. Knobloch, Eine neue Methode zur Approximation periodischer Lösungen nicht-linearer Differentialgleichungen zweiter Ordnung, Math. Z. 82 (1963), 177-197.
  • [7] A. Lepin and L. Lepin, Boundary Value Problems for Ordinary Differential Equations of the Second Order, Zinatne, Riga, 1988 (in Russian).
  • [8] J. Mawhin, Topological Degree Methods in Nonlinear BVPs, CBMS Regional Conf. Ser. in Math. 40, Providence, R.I., 1979.
  • [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.
  • [10] J. J. Nieto, Nonlinear second order periodic boundary value problems, J. Math. Anal. Appl. 130 (1988), 22-29.
  • [11] P. Omari, Non-ordered lower and upper solutions and solvability of the periodic problem for the Liénard and the Rayleigh equations, Rend. Inst. Mat. Univ. Trieste 20 (1988), 54-64.
  • [12] I. Rachůnková, The first kind periodic solutions of differential equations of the second order, Math. Slovaca 39 (1989), 407-415.
  • [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.
  • [14] I. Rachůnková, On a transmission problem, Acta Univ. Palack. Olomuc. Fac. Rerum Nat. 105, Math. 31 (1992), 45-59.
  • [15] I. Rachůnková, On resonance problems for the second order differential equations, preprint.
  • [16] R. Reissig, Schwingungssätze für die verallgemeinerte Liénardsche Differentialgleichung, Abh. Math. Sem. Univ. Hamburg 44 (1975), 45-51.
  • [17] N. I. Vasil'ev and Yu. A. Klokov, Foundations of the Theory of Boundary Value Problems for Ordinary Differential Equations, Zinatne, Riga, 1978 (in Russian).
  • [18] F. Zanolin, Periodic solutions for differential systems of Rayleigh type, Rend. Inst. Mat. Univ. Trieste 12 (1980), 69-77.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv65z3p235bwm
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