Existence local and global solution of multipoint Cauchy problem for nonlocal nonlinear equations

Abstract

In this paper, the multipoint Cauchy problem for nonlocal nonlinear wave type equatıons are studied.The equation involves a convolution integral operator with a general kernel function whose Fourier transform is nonnegative. We establish local and global existence and uniqueness of solutions assuming enough smoothness on the initial data together with some growth conditions on the nonlinear term

arXiv admin note: substantial text overlap with arXiv:1901.04589, arXiv:1706.00813, arXiv:1707.04492