# On existence and uniqueness of solutions of nonlocal problems for hyperbolic differential-functional equations in two independent variables

Annales Polonici Mathematici (1997)

- Volume: 67, Issue: 3, page 205-214
- ISSN: 0066-2216

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topTomasz Człapiński. "On existence and uniqueness of solutions of nonlocal problems for hyperbolic differential-functional equations in two independent variables." Annales Polonici Mathematici 67.3 (1997): 205-214. <http://eudml.org/doc/270667>.

@article{TomaszCzłapiński1997,

abstract = {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.},

author = {Tomasz Człapiński},

journal = {Annales Polonici Mathematici},

keywords = {differential-functional equations; nonlinear hyperbolic problems; nonlocal conditions; classical solutions; existence; uniqueness; unbounded domains},

language = {eng},

number = {3},

pages = {205-214},

title = {On existence and uniqueness of solutions of nonlocal problems for hyperbolic differential-functional equations in two independent variables},

url = {http://eudml.org/doc/270667},

volume = {67},

year = {1997},

}

TY - JOUR

AU - Tomasz Człapiński

TI - On existence and uniqueness of solutions of nonlocal problems for hyperbolic differential-functional equations in two independent variables

JO - Annales Polonici Mathematici

PY - 1997

VL - 67

IS - 3

SP - 205

EP - 214

AB - 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.

LA - eng

KW - differential-functional equations; nonlinear hyperbolic problems; nonlocal conditions; classical solutions; existence; uniqueness; unbounded domains

UR - http://eudml.org/doc/270667

ER -

## References

top- [1] L. Byszewski, Strong maximum and minimum principles for parabolic problems with nonlocal inequalities, Z. Angew. Math. Mech. 70 (1990), 202-205. Zbl0709.35018
- [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. Zbl0725.35059
- [3] J. Chabrowski, On non-local problems for parabolic equations, Nagoya Math. J. 93 (1984), 109-131. Zbl0506.35048
- [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. Zbl0859.35131
- [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. Zbl0658.35003
- [8] W. Walter, Differential and Integral Inequalities, Springer, Berlin, 1970.

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