Description
| - The paper provides an existence principle for the Sturm--Liouville boundary value problem with state-dependent impulses z''(t) = f(t,z(t),z'(t)) for a.e. t in [0,T] z(0) - az'(0) = c_1, z(T) + bz'(T) = c_2, z(tau_i+) - z(tau_i) = J_i(tau_i,z(tau_i)), z'(tau_i+) - z'(tau_i-) = M_i(tau_i,z(tau_i)), where the points tau_1, ..., tau_p depend on z through the equations tau_ = gamma(tau_i)), i = 1,...,p, p in N. Provided a, b in [0,infty), c_j in R, j = 1,2, and the data functions f, J_i, M_i, i=1,...,p, are bounded, transversality conditions for barriers gamma_i, i = 1,...,p, which yield the solvability of the problem, are delivered. An application to the problem with unbounded data functions is demonstrated.
- The paper provides an existence principle for the Sturm--Liouville boundary value problem with state-dependent impulses z''(t) = f(t,z(t),z'(t)) for a.e. t in [0,T] z(0) - az'(0) = c_1, z(T) + bz'(T) = c_2, z(tau_i+) - z(tau_i) = J_i(tau_i,z(tau_i)), z'(tau_i+) - z'(tau_i-) = M_i(tau_i,z(tau_i)), where the points tau_1, ..., tau_p depend on z through the equations tau_ = gamma(tau_i)), i = 1,...,p, p in N. Provided a, b in [0,infty), c_j in R, j = 1,2, and the data functions f, J_i, M_i, i=1,...,p, are bounded, transversality conditions for barriers gamma_i, i = 1,...,p, which yield the solvability of the problem, are delivered. An application to the problem with unbounded data functions is demonstrated. (en)
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