Abstract
This paper is concerned with a class of boundary value problems of the impulsive differential equations with one-dimensional p-Laplacian on whole line with a nonCarathéeodory nonlinearity. Sufficient conditions to guarantee the existence of solutions are established. Some examples are given to illustrate the main results.
Highlights
The motivation for the present work stems from both practical and theoretical aspects
It is of great interest to investigate, in particular, the existence of solutions with prescribed asymptotic behavior, which are global in the sense that they are solutions on the whole line
The existence of global solutions with prescribed asymptotic behavior is usually formulated as the existence of solutions of boundary value problems on the whole line
Summary
The motivation for the present work stems from both practical and theoretical aspects. M is relatively compact if and only if the following conditions are satisfied: (i) both {t → x(t)/σ(t): x ∈ M } and {t → ρ(t)x (t)/Φ−1(τ (t)): x ∈ M } are uniformly bounded; (ii) both {t → x(t)/σ(t): x ∈ M } and {t → ρ(t)x (t)/Φ−1(τ (t)): x ∈ M } are equicontinuous in (ts, ts+1] (s ∈ N ); (iii) both {t → x(t)/σ(t): x ∈ M } and {t → ρ(t)x (t)/Φ−1(τ (t)): x ∈ M } are equi-convergent as t → ±∞.
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