Dirichlet boundary value problem for differential equation with ϕ-Laplacian and state-dependent impulses

2017 ◽  
Vol 67 (2) ◽  
Author(s):  
Jan Tomeček
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Dirichlet Boundary Value Problem ◽  
State Dependent

AbstractThe paper deals with the boundary value problem for differential equation with

Second order BVPs with state dependent impulses via lower and upper functions

2014 ◽  
Vol 12 (1) ◽  
Author(s):  
Irena Rachůnková ◽  
Jan Tomeček
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Dirichlet Boundary Value Problem ◽  
State Dependent ◽  
Lower And Upper Functions

AbstractThe paper deals with the following second order Dirichlet boundary value problem with p ∈ ℕ state-dependent impulses: z″(t) = f (t,z(t)) for a.e. t ∈ [0, T], z(0) = z(T) = 0, z′(τ i+) − z′(τ i−) = I i(τ i, z(τ i)), τ i = γ i(z(τ i)), i = 1,..., p. 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.

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