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.
@article{bwmeta1.element.bwnjournal-article-apmv67z3p205bwm, author = {Tomasz Cz\l api\'nski}, title = {On existence and uniqueness of solutions of nonlocal problems for hyperbolic differential-functional equations in two independent variables}, journal = {Annales Polonici Mathematici}, volume = {66}, year = {1997}, pages = {205-214}, zbl = {0899.35120}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv67z3p205bwm} }
Tomasz Człapiński. On existence and uniqueness of solutions of nonlocal problems for hyperbolic differential-functional equations in two independent variables. Annales Polonici Mathematici, Tome 66 (1997) pp. 205-214. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv67z3p205bwm/
[000] [1] L. Byszewski, Strong maximum and minimum principles for parabolic problems with nonlocal inequalities, Z. Angew. Math. Mech. 70 (1990), 202-205. | Zbl 0709.35018
[001] [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. | Zbl 0725.35059
[002] [3] J. Chabrowski, On non-local problems for parabolic equations, Nagoya Math. J. 93 (1984), 109-131. | Zbl 0506.35048
[003] [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.
[004] [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. | Zbl 0859.35131
[005] [6] M. Krzyżański, Partial Differential Equations of Second Order, Vol. 2, Polish Sci. Publ., Warszawa, 1971.
[006] [7] G. S. Ladde, V. Lakshmikantham and A. S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman Adv. Publ. Program, Boston, 1985. | Zbl 0658.35003
[007] [8] W. Walter, Differential and Integral Inequalities, Springer, Berlin, 1970.