EXISTENCE AND UNIQUENESS OF SOLUTIONS OF THE DIRICHLET NONLOCAL PROBLEM WITH NONLOCAL INITIAL CONDITION

Ludwik Byszewski,

Teresa Winiarska

Abstrakt

The aim of this paper is to prove the existence and uniqueness of solutions of the Dirichlet nonlocal problem with nonlocal initial condition. The considerations are extensions of results by E. Andreu-Vaillo, J. M. Mazón, J. D. Rossi and J. J. Toledo-Melero [1].

Słowa kluczowe: existence and uniqueness of solutions, Dirichlet problem, nonlocal problem, nonlocal initial condition
References

Andreu-Vaillo F., Mazón J. M., Rossi J. D., Toledo-Melero J. J., Nonlocal Diffusion Problems, American Mathematical Society, Providence, Rhode Island 2010.

Kamont Z., Ordinary Differential Equations, Wydawnictwo Uniwersytetu Gdanskiego, Gdansk 1999 [in Polish].

Muszynski J., Myszkis A. D., Ordinary Differential Equations, Panstwowe Wydawnictwo Naukowe, Warszawa 1984 [in Polish].

Pelczar A., Szarski J., Introduction to the Theory of Differential Equations, Panstwowe Wydawnictwo Naukowe, Warszawa 1987 [in Polish].