On solvability of boundary value problems for higher order nonlinear hyperbolic equations Original Research Article

In the rectangle Ω=[0,a]×[0,b]Ω=[0,a]×[0,b] for the nonlinear hyperbolic equation View the MathML sourceu(m,n)=∑i=0m−1h1i(x)u(i,n)+∑k=0n−1h2k(y)u(m,k)+f(x,y,u,…,u(m−1,n−1)) Turn MathJax on the boundary value problems of the type View the MathML sourcel1i(u(⋅,y))=0(i=1,…,m),l2k(u(x,⋅))=0(k=1,…,n) Turn MathJax on are considered, where View the MathML sourcel1i:Cm−1([0,a])→R(i=1,…,m) and View the MathML sourcel2k:Cn−1([0,b])→R(k=1,…,n) are linear bounded functionals. Sufficient conditions of solvability and unique solvability of the general problem and its particular cases (Nicoletti type, Dirichlet, Lidstone and Periodic problems) are established.