Abstract and Applied Analysis

Multiple Solutions for Boundary Value Problems of $n$th-Order Nonlinear Integrodifferential Equations in Banach Spaces

Yanlai Chen

Abstract

The boundary value problems of a class of $n$th-order nonlinear integrodifferential equations of mixed type in Banach space are considered, and the existence of three solutions is obtained by using the fixed-point index theory.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 296038, 7 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393512118

Digital Object Identifier
doi:10.1155/2013/296038

Mathematical Reviews number (MathSciNet)
MR3126761

Zentralblatt MATH identifier
1296.34150

Citation

Chen, Yanlai. Multiple Solutions for Boundary Value Problems of $n$ th-Order Nonlinear Integrodifferential Equations in Banach Spaces. Abstr. Appl. Anal. 2013 (2013), Article ID 296038, 7 pages. doi:10.1155/2013/296038. https://projecteuclid.org/euclid.aaa/1393512118

References

• D. Guo, “Integro-differential equations on unbounded domains in Banach spaces,” Chinese Annals of Mathematics. Series B, vol. 20, no. 4, pp. 435–446, 1999.
• Y. Chen and B. Qin, “Multiple positive solutions for first-order impulsive singular integro-differential equations on the half line in a Banach space,” Boundary Value Problems, vol. 2013, article 69, 24 pages, 2013.
• Y. Liu, “Positive solutions of second order singular initial value problem in Banach space,” Indian Journal of Pure and Applied Mathematics, vol. 33, no. 6, pp. 833–845, 2002.
• Y. L. Chen and B. X. Qin, “Multiple solutions of singular boundary value problems for nonlinear integro-differential equations in Banach spaces,” Journal of Systems Science and Mathematical Sciences, vol. 25, no. 5, pp. 550–561, 2005.
• D. Guo, “Existence of positive solutions for nth-order nonlinear impulsive singular integro-differential equations in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 9, pp. 2727–2740, 2008.
• D. Guo, “Positive solutions of an infinite boundary value problem for nth-order nonlinear impulsive singular integro-differential equations in Banach spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 5, pp. 2078–2090, 2009.
• D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, vol. 5 of Notes and Reports in Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1988.
• D. Guo, V. Lakshmikantham, and X. Liu, Nonlinear Integral Equations in Abstract Spaces, vol. 373 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.