Differential-functional Goursat problem

• Autorzy: Wojciechowski R.
• Języki publikacji: EN

Abstrakty

EN

This paper is devoted to a differential-functional Goursat problem for second-order hyperbolic equations. There are proved existence results based on the Banach and Schauder fixed point theorems with some Bielecki type norms.

Słowa kluczowe

EN

words and phrases; functional differential equation

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2007
• Tom: Vol. 47, [Z] 2
• Strony: 127--140
• Opis fizyczny: bibliogr. 17 poz.

Twórcy

autor

Wojciechowski R.

• Remigiusz Wojciechowski University of Gdańsk ul. Wita Stwosza 57,

Bibliografia

• [1] A. Bielecki, Une remarque sur l'application de la m´ethode de Banach-Cacciopoli-Tikhonov dans la th´eorie de l'´equation s =f(x, y, x, p, q), Bull. Acad. Polon. Sci. Cl. III 4 (1956), 265-268.
• [2] A. Bielecki, Une remarque sur la m´ethode de Banach-Cacciopoli-Tikhonov dans la théorie des équations diff´erentielles ordinaires, Bull. Acad. Polon. Sci. Cl. III 4 (1956), 261-264.
• [3] L. Byszewski, Existence and uniqueness of classical solutions to semilinear Darboux problems together with nonstandard conditions with integrals (English summary), Comment. Math. Prace Mat. 43(2) (2003), 169-183.
• [4] 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(3) (1990), 163-168.
• [5] L. Byszewski and V. Lakshmikantham, Monotone iterative technique for nonlocal hyperbolic differential problem (English summary), J. Math. Phys. Sci. 26(4) (1992), 345-359.
• [6] L. Byszewski and N.S. Papageorgiou, An application of a noncompactness technique to an investigation of the existence of solutions to a nonlocal multivalued Darboux problem (English summary), J. Appl. Math. Stochastic Anal. 12(2) (1999), 179-190.
• [7] T. Człapiński, On existence and uniqueness of solutions of nonlocal problems for hyperbolic differential-functional equations in two independent variables (English summary), Ann. Polon. Math. 67(3) (1997), 205-214.
• [8] T. Człapiński, On the Darboux problem for partial differential-functional equations with infinite delay at derivatives, Nonlinear Anal. 44(3) (2001), Ser. A: Theory Methods, 389-398.
• [9] T. Człapiński, On the local Cauchy problem for nonlinear hyperbolic functional-differential equations (English summary), Ann. Polon. Math. 67(3) (1997), 215-232.
• [10] Z. Kamont, H. Leszczyński, Numerical solutions to the Darboux problem with functional dependence (English summary), Georgian Math. J. 5(1) (1998), 71-90.
• [11] M. Kwapisz, J. Turo, Existence and uniqueness of solution for some integral-functional equation, Comment. Math. Prace Mat. 23(2) (1983), 259-267.
• [12] M. Kwapisz M., J. Turo, On some class of non-linear functional equations, Ann. Polon. Math. 34 (1977), no. 1, 85-95.
• [13] M. Kwapisz and J. Turo, On the existence and uniqueness of intagrable solutions of functional equations in a Banach space, Aequationes Math. 19 (1979), no. 1, 53-65.
• [14] V. Lakshmikantham, S. Koksal and S. Melbourne, Monotone Flows and Rapid Convergence for Nonlinear Partial Differential, Taylor & Francis Ltd.
• [15] A. Pelczar, On the method of successive approximations for some operator equations with applications to partial differential hyperbolic equations, Zeszyty Nauk. Univ. Jagiello. Prace Mat. Zeszyt 11 (1966), 59-68.
• [16] A. Pelczar, Some functional differential equations. Dissertationes Math. 100 1973.
• [17] W. Walter, Differential and integral inequelities, Springer-Verlag Berlin-Heilelberg-New York 1970.