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

## TL;DR

This paper investigates the existence and uniqueness of local and global solutions for multipoint Cauchy problems involving nonlocal nonlinear wave equations with convolution operators, under certain smoothness and growth conditions.

## Contribution

It provides new results on the existence and uniqueness of solutions for a class of nonlocal nonlinear wave equations with general kernel functions.

## Key findings

- Established local and global existence of solutions.
- Proved uniqueness of solutions under specified conditions.
- Extended the theory to equations with general convolution kernels.

## Abstract

In this paper, the multipoint Cauchy problem for nonlocal nonlinear wave type equat{\i}ons 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