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1998 | 69 | 3 | 265-270
Tytuł artykułu

Multiple positive solutions of a nonlinear fourth order periodic boundary value problem

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The fourth order periodic boundary value problem $u^{(4)} - m⁴u + F(t,u) = 0$, 0 < t < 2π, with $u^{(i)}(0) = u^{(i)}(2π)$, i = 0,1,2,3, is studied by using the fixed point index of mappings in cones, where F is a nonnegative continuous function and 0 < m < 1. Under suitable conditions on F, it is proved that the problem has at least two positive solutions if m ∈ (0,M), where M is the smallest positive root of the equation tan mπ = -tanh mπ, which takes the value 0.7528094 with an error of $±10^{-7}$.
Rocznik
Tom
69
Numer
3
Strony
265-270
Opis fizyczny
Daty
wydano
1998
poprawiono
1997-04-21
otrzymano
1997-10-09
Twórcy
autor
  • Department of Mathematics, Daqing Petroleum Institute, Anda 151400, Heilongjiang, P.R. China
autor
  • Department of Mathematics, Northeast Normal University, Changchun 130024, P.R. China
Bibliografia
  • [1] A. Cabada, The method of lower and upper solutions for second, third, fourth and higher order boundary value problems, J. Math. Anal. Appl. 185 (1994), 302-320.
  • [2] 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.
  • [3] L. H. Erbe, S. C. Hu and H. Y. Wang, Multiple positive solutions of some boundary value problems, J. Math. Anal. Appl. 184 (1994), 640-648.
  • [4] W. J. Gao and J. Y. Wang, On a nonlinear second order periodic boundary value problem with Carathéodory functions, Ann. Polon. Math. 62 (1995), 283-291.
  • [5] D. Q. Jiang and J. Y. Wang, A generalized periodic boundary value problem for the one-dimensional p-Laplacian, Ann. Polon. Math. 65 (1997), 265-270.
  • [6] V. Šeda, J. J. Nieto and M. Gera, Periodic boundary value problems for nonlinear higher order ordinary differential equations, Appl. Math. Comput. 48 (1992), 71-82.
  • [7] 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv69z3p265bwm
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