THE NONLOCAL SOLVABILITY CONDITIONS FOR A SYSTEM WITH CONSTANT TERMS AND COEFFICIENTS OF THE VARIABLE

We consider the Cauchy problem for a system of quasilinear differential equations with constant terms and coefficients of the variable t. We investigate the solvability of the Cauchy problem for a system of quasilinear differential equations with constant terms and coefficients of the variable t using the additional argument method. A theorem on the existence and uniqueness of the local solution of the Cauchy problem for a system of quasilinear differential equations with constant terms and coefficients of the variable t is formulated. We obtain sufficient conditions for the existence and uniqueness of a nonlocal solution of the Cauchy problem in original coordinates for a system of quasilinear differential equations with constant terms and coefficients of the variable t. A theorem on the existence and uniqueness of the nonlocal solution of the Cauchy problem for a system of quasilinear differential equations with constant terms and coefficients of the variable t is formulated. A theorem on the existence and uniqueness of the nonlocal solution of the Cauchy problem for a system of quasilinear differential equations with constant terms and coefficients of the variable t is proved. The proof of the nonlocal solvability of the Cauchy problem for a system of quasilinear differential equations with constant terms and coefficients of the variable t relies on global estimates.