Displaying similar documents to “Second order BVPs with state dependent impulses via lower and upper functions”

A survey and some new results on the existence of solutions of IPBVPs for first order functional differential equations

Yuji Liu (2009)

Applications of Mathematics

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This paper deals with the periodic boundary value problem for nonlinear impulsive functional differential equation x ' ( t ) = f ( t , x ( t ) , x ( α 1 ( t ) ) , , x ( α n ( t ) ) ) for a.e. t [ 0 , T ] , Δ x ( t k ) = I k ( x ( t k ) ) , k = 1 , , m , x ( 0 ) = x ( T ) . We first present a survey and then obtain new sufficient conditions for the existence of at least one solution by using Mawhin’s continuation theorem. Examples are presented to illustrate the main results.

Periodic BVP with φ -Laplacian and impulses

Vladimír Polášek (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The paper deals with the impulsive boundary value problem d d t [ φ ( y ' ( t ) ) ] = f ( t , y ( t ) , y ' ( t ) ) , y ( 0 ) = y ( T ) , y ' ( 0 ) = y ' ( T ) , y ( t i + ) = J i ( y ( t i ) ) , y ' ( t i + ) = M i ( y ' ( t i ) ) , i = 1 , ... m . The method of lower and upper solutions is directly applied to obtain the results for this problems whose right-hand sides either fulfil conditions of the sign type or satisfy one-sided growth conditions.