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Multiplicity of solutions for impulsive differential equation on the half-line via variational methods. (English) Zbl 1334.34062

Summary: 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.

MSC:

34B37 Boundary value problems with impulses for ordinary differential equations
34B08 Parameter dependent boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
58E30 Variational principles in infinite-dimensional spaces
34B40 Boundary value problems on infinite intervals for ordinary differential equations
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