# Solvability of the nonlocal multi-point boundary value problem

Subject | Local and nonlocal boundary value problems for partial differential equations |

Title | Solvability of the nonlocal multi-point boundary value problem |

Author(s) | Anar Asanova |

Keywords | multi-point boundary value problem, hyperbolic equation, solvability |

Abstract | Abstract: In this study, we consider the multi-point boundary value problem on
¯Ω=[0,T]×[0,ω] for the second-order system of quasilinear hyperbolic equations
{■((∂^2 u)/∂x∂t=A(t,x) ∂u/∂x+f(t,x,u,∂u/∂t), @u=(u_1,…,u_n )∈R^n ,(t,x)∈¯Ω,@∑_(i=0)^m▒〖P_i (x) 〗 u(t_i,x)=φ(x), x∈[0,ω],@u(t,0)=ψ(t), t∈[0,T],)┤ (1)
where n ×n matrix A(t,x) is continuous on ¯Ω, n ×n matrices P_i (x), n vector-function φ(x) are continuously differentiable on [0,ω], i=¯(0,m) ,
0=t_0 |