Solvability of Boundary Value Problems for Second Order Impulsive Differential Equations on Whole Line with a Non-Carathédory Nonlinearity
Mathematica Moravica, Tome 20 (2016) no. 1.

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We study a class of boundary value problems of the impulsive differential equations on whole lines with a non-Carathéodory nonlinearity. Sufficient conditions to guarantee the existence of solutions are established. A new Banach function space X and its relatively compact property of subset of X is proved. An example is given to illustrate the main results.
Mots-clés : Second order impulsive differential equation, boundary value problem, non-Carathéodory nonlinearity, fixed point theorem 
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     title = {Solvability of {Boundary} {Value} {Problems} for {Second} {Order} {Impulsive} {Differential} {Equations} on {Whole} {Line} with a {Non-Carath\'edory} {Nonlinearity}},
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Xiaohu Yang; Yuji Liu. Solvability of Boundary Value Problems for Second Order Impulsive Differential Equations on Whole Line with a Non-Carathédory Nonlinearity. Mathematica Moravica, Tome 20 (2016) no. 1. https://geodesic-test.mathdoc.fr/item/MM3_2016_20_1_a3/