Abstract
In this paper, we study the multiple solutions for some second-order p-Laplace differential equations with three-point boundary conditions and instantaneous and noninstantaneous impulses. By applying the variational method and critical point theory the multiple solutions are obtained in a Sobolev space. Compared with other local boundary value problems, the three-point boundary value problem is less studied by variational method due to its variational structure. Finally, two examples are given to illustrate the results of multiplicity.
Highlights
In recent years, the research on impulsive differential equations have attracted widespread attention
Impulsive differential equations have been widely used in recent years, especially, in the field of biological mathematics
In the study of pharmacokinetic model, since oral and injected drugs often enter the human body in the form of impulse, it is more reasonable to use impulse differential equations to describe the changes of drug concentration in the human body
Summary
The research on impulsive differential equations have attracted widespread attention. Due to its wide range of applications, some scholars began to study the existence of solutions of differential equations with instantaneous and noninstantaneous impulses, and through fixed point theorems, upper and lower solution theorems, variational methods, etc., they obtained some excellent results [1, 3, 4, 6,7,8, 10, 11, 13,14,15,16,17,18,19]. Tian and Zhang in [15] studied the existence of classical solutions for differential equations with instantaneous and noninstantaneous impulses, they considered the following problem:.
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