Vol. 13, No. 1, 2020

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Solutions of periodic boundary value problems

R. Aadith, Paras Gupta and Jagan Mohan Jonnalagadda

Vol. 13 (2020), No. 1, 99–107
Abstract

We deal with a resonant boundary value problem involving a second-order differential equation with periodic boundary conditions. First, we modify the problem at resonance and consider an equivalent nonresonant boundary value problem. Next, we obtain sufficient conditions for the existence of solutions of the modified boundary value problem, using fixed-point theory. Consequently, these conditions suffice for the existence of solutions of the original boundary value problem. We demonstrate the applicability of established results through examples.

Keywords
boundary value problem, resonance, shift, Green's function, fixed point, existence
Mathematical Subject Classification 2010
Primary: 34B15
Secondary: 34B27
Milestones
Received: 21 March 2019
Revised: 5 April 2019
Accepted: 20 September 2019
Published: 4 February 2020

Communicated by Hari Mohan Srivastava
Authors
R. Aadith
Department of Mathematics
Birla Institute of Technology and Science Pilani
Hyderabad
India
Paras Gupta
Department of Mathematics
Birla Institute of Technology and Science Pilani
Hyderabad
India
Jagan Mohan Jonnalagadda
Department of Mathematics
Birla Institute of Technology and Science Pilani
Hyderabad
India