Abstract
In this paper, the existence of solutions for a second-order impulsive differential equation with two parameters on the half-line is investigated. Applying variational methods, we give some new criteria to guarantee that the impulsive problem has at least one classical solution, three classical solutions and infinitely many classical solutions, respectively. Some recent results are extended and significantly improved. Two examples are presented to demonstrate the application of our main results.
Highlights
Boundary value problems (BVPs) on the half-line occur in many applications; see [ – ]
Impulsive differential equations have been widely applied in biology, control theory, industrial robotics, medicine, population dynamics and so on; see [ – ]
A lot of work has been done in the theory of impulsive differential equations, we refer the reader to [ – ]
Summary
1 Introduction In this paper, we consider the following boundary value problem with impulses: Assume that (A ) (or (A )), (A ) hold and the following conditions are satisfied. (A ) There exists a constant m satisfying Assume that the following conditions are satisfied.
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