We seek for classical solutions to hyperbolic nonlinear partial differential-functional equations of the second order. We give two theorems on existence and uniqueness for problems with nonlocal conditions in bounded and unbounded domains.
Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
Bibliografia
[1] L. Byszewski, Strong maximum and minimum principles for parabolic problems with nonlocal inequalities, Z. Angew. Math. Mech. 70 (1990), 202-205.
[2] L. Byszewski, Existence and uniqueness of solutions of nonlocal problems for hyperbolic equation uₓt = F(x,t,u,uₓ), J. Appl. Math. Stochastic Anal. 3 (1990), 163-168.
[3] J. Chabrowski, On non-local problems for parabolic equations, Nagoya Math. J. 93 (1984), 109-131.
[4] H. Chi, H. Poorkarmi, J. Wiener and S. M. Shah, On the exponential growth of solutions to nonlinear hyperbolic equations, Internat. J. Math. Math. Sci. 12 (1989), 539-546.
[5] T. Człapiński, Existence of solutions of the Darboux problem for partial differential-functional equations with infinite delay in a Banach space, Comment. Math. 35 (1995), 111-122.
[6] M. Krzyżański, Partial Differential Equations of Second Order, Vol. 2, Polish Sci. Publ., Warszawa, 1971.
[7] G. S. Ladde, V. Lakshmikantham and A. S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman Adv. Publ. Program, Boston, 1985.
[8] W. Walter, Differential and Integral Inequalities, Springer, Berlin, 1970.