Abstract
In this paper, by using the coincidence degree theory and the upper and lower solutions method, we deal with the existence of multiple solutions to three-point boundary value problems for second-order differential equation with impulses at resonance. An example is given to show the validity of our results.
Highlights
1 Introduction The purpose of the present paper is to investigate the following second-order impulsive differential equations:
Impulsive differential equations describe processes which experience a sudden change of their state at certain moments
The theory of impulse differential equations has been a significant development in recent years and played a very important role in modern applied mathematical models of real processes rising in phenomena studied in physics, population dynamics, chemical technology, biotechnology, and economics; see [ – ] and the references therein
Summary
Gupta et al made use of the Leray-Schauder continuation theorem to get the results on the existence of the solution for the problems We assume that there exist n (n ∈ N and n ≥ ) pairs of upper and lower solutions for problem By considering a suitably modified nonlinearity and applying the coincidence degree method of Mawhin [ ], the existence of multiple solutions for the problem
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