Solvability of a class of boundary value problems in the space of convergent sequences

Abstract

We consider two types of infinite systems of second-order differential equations with boundary conditions in the Banach sequence space c. For each system, sufficient conditions are provided for the existence of solutions. Our approach is based on the use of measure of noncompactness concept and the application of Darbo’s theorem for condensing operators. Some examples are presented to illustrate the obtained results.

Keywords:

• Infinite system
• differential equations
• Banach sequence space
• measures of noncompactness
• Darbo’s theorem

AMS Subject Classifications:

• 93C15
• 47H08
• 46B45

Acknowledgements

The third author extends his appreciation to Distinguished Scientist Fellowship Program (DSFP) at King Saud University (Saudi Arabia).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the King Saud University.