The boundary value problem of higher order differential equations with delay

• Autorzy: He Z. , Shen J.
• Języki publikacji: EN

Abstrakty

EN

In the paper, Guo–Krasnoselskii’s fixed point theorem is adapted to study the existence of positive solutions to a class of boundary value problems for higher order differential equations with delay. The sufficient conditions, which assure that the equation has one positive solution or two positive solutions, are derived. These conclusions generalize some existing ones.

Słowa kluczowe

EN

higher order differential equation with p-Laplacian; boundary value problem; positive solution; fixed-point theorem

PL

równania różniczkowe wyższego rzędu; problem wartości granicznej; pozytywne rozwiązanie; twierdzenie stałoprzecinkowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2013
• Tom: Vol. 46, nr 1
• Strony: 87--100
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

He Z.

• College of Science, Zhejiang Forestry University, Hangzhou, Zhejiang 311300, P.R. China

autor

Shen J.

• Department of Mathematics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, P.R. China

Bibliografia

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• [6] D. Bai, Y. Xu, Existence of positive solutions for boundary-value problems of second-order delay differential equations, Appl. Math. Lett. 18 (2005), 621–630.
• [7] W. B. Wang, J. H. Shen, Positive solutions to a multi-point boundary value problem with delay, Appl. Math. Comput. 188 (2007), 96–102.
• [8] T. Jankowski, Solvability of three point boundary value problems for second order ordinary differential equations with deviating arguments, J. Math. Anal. Appl. 312 (2005), 620–636.
• [9] B. Du, X. P. Hu, W. G. Ge, Positive solutions to a type of multi-point boundary value problem with delay and one-dimensional p-Laplacian, Appl. Math. Comput. 208 (2009), 501–510.
• [10] J. R. Graef, B. Yang, Positive solutions to a multi-point higher order boundary-value problem, J. Math. Anal. Appl. 316 (2006), 409–421.
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• [12] D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, New York, 1988.
• [13] J. Henderson, Boundary Value Problems for Functional Equations, World Scientific, 1995.