On the Picard problem for hyperbolic differential equations in Banach spaces

• Autorzy: Antoni Sadowski
• Języki publikacji: EN

Abstrakty

EN

B. Rzepecki in [5] examined the Darboux problem for the hyperbolic equation $z_{xy} = f(x,y,z,z_{xy})$ on the quarter-plane x ≥ 0, y ≥ 0 via a fixed point theorem of B.N. Sadovskii [6]. The aim of this paper is to study the Picard problem for the hyperbolic equation $z_{xy} = f(x,y,z,z_x,z_{xy})$ using a method developed by A. Ambrosetti [1], K. Goebel and W. Rzymowski [2] and B. Rzepecki [5].

Słowa kluczowe

EN

boundary value problem; fixed point theorem; functional-integral equation; hyperbolic equation; measure of noncompactness

Kategorie tematyczne

• 35L70: Nonlinear second-order hyperbolic equations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2003
• Tom: 23
• Numer: 1
• Strony: 31-37

Daty

wydano

2003

otrzymano

2003-04-25

Twórcy

autor

Antoni Sadowski

• Institute of Mathematics and Physics, Technical University of Warsaw, Branch Płock, ul. Łukasiewcza 17, 09-400 Płock, Poland

Bibliografia

• [1] A. Ambrosetti, Un teorema di essistenza per le equazioni differenziali nagli spazi di Banach, Rend. Sem. Mat. Univ. Padova 39 (1967), 349-360.
• [2] K. Goebel, W. Rzymowski, An existence theorem for the equations x' = f(t,x) in Banach space, Bull. Acad. Polon. Sci., Sér. Sci. Math. 18 (1970), 367-370.
• [3] P. Negrini, Sul problema di Darboux negli spazi di Banach, Bolletino U.M.I. (5) 17-A (1980), 156-160.
• [4] B. Rzepecki, Measure of Non-Compactness and Krasnoselskii's Fixed Point Theorem, Bull. Acad. Polon. Sci., Sér. Sci. Math. 24 (1976), 861-866.
• [5] B. Rzepecki, On the existence of solution of the Darboux problem for the hyperbolic partial differential equations in Banach Spaces, Rend. Sem. Mat. Univ. Padova 76 (1986).
• [6] B.N. Sadovskii, Limit compact and condensing operators, Russian Math. Surveys 27 (1972), 86-144.

Identyfikatory

DOI

10.7151/dmgt.1044