Abstract:The paper deals with the following second order Dirichlet boundary value problem with ∈ N state-dependent impulses:. Solvability of this problem is proved under the assumption that there exists a well-ordered couple of lower and upper functions to the corresponding Dirichlet problem without impulses.
MSC:34B37, 34B15
The paper provides an existence principle for a general boundary value problem of the form, where the impulse points t are determined as solutions of the equations. . , c n ∈ R, the functions a j /a n , j = 0, . . .
The paper provides an existence principle for a general boundary value problem of the form, where the impulse points t are determined as solutions of the equations. . , c n ∈ R, the functions a j /a n , j = 0, . . .
The paper investigates a fixed point problem in the space (W 1,∞ ([a, b]; R n )) p+1 which is connected to boundary value problems with state-dependent impulses of the formHere, the impulse instants τ i are determined as solutions of the equations Provided the data functions f and J i are bounded, transversality conditions which guarantee that this fixed point problem is solvable are presented. As a result it is possible to realize the construction of a solution of the above impulsive problem.
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