On nonlinear integral equations in some functions spaces

• Autorzy: Bardaro C. , Musielak J. , Vinti G.
• Języki publikacji: EN

Abstrakty

EN

There are established some conditions for existence of solutions of a nonlinear integral equation Tf =f+g, where T is a convolution-type integral operator.

Słowa kluczowe

EN

integral equations; compact operator; Orlicz space; modular space

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 3
• Strony: 583--592
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Bardaro C.

• Dipartimento di Matematica e Informatica, Universitá Degli Studi, Via Vanvitelli, 1, 06123 Perugia, Italy

autor

Musielak J.

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznan, Poland

autor

Vinti G.

• Dipartimento di Matematica e Informatica, Universitá Degli Studi, Via Vanvitelli, 1, 06123 Perugia, Italy

Bibliografia

• [1] C. Bardaro, J. Musielak, G. Vinti, On absolute continuity of a modular connected with strong summability, Commentationes Math. 34, (1994), 21-33.
• [2] C. Bardaro, J. Musielak, G. Vinti, On the definition and properties of a general modulus of continuity in some functional spaces, Math. Japonica 43, (1996), 445-450.
• [3] C. Bardaro, J. Musielak, G. Vinti, On nonlinear integro-differential operators in generalized Orlicz-Sobolev spaces, J. Approximation Theory, 105 N. 2, (2000), 238-251.
• [4] C. Bardaro, G. Vinti, On the order of modular approximation for nets of integral operators in modular Lipschitz classes, Functiones & Approximate, special volume dedicated to Prof. J. Musielak, 26, (1998), 139-154.
• [5] N. Dunford, J. T. Schwartz, Linear Operators, Part I, General Theory, Wiley (z Sons, New York, 1958.
• [6] D. Guo, V. Lakshmikantham, X. Liu, Nonlinear Integral Equations in Abstract Spaces, Kluwer Acad. Publ., 1996.
• [7] A. Kaminska, On some compactness criterion for Orlicz subspaces Εφ(Ω), Commentationes Math. 22, (1981), 126-136.
• [8] A. Kaminska, R. Pluciennik, Some theorems on compactness in generalized Orlicz spaces with application of the Δ∞-condition, Functiones et Approximate 10, (1980), 135-146.
• [9] M. A. Krasnosel'skii, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, Oxford, 1964.
• [10] M. A. Krasnosel'skii, Y. B. Rutickii, Convex Functions and Orlicz Spaces, P. Noordhoff Ltd, Groningen, 1961.
• [11] A. Musielak, J. Musielak, On nonlinear integral operators in function spaces, Math. Japonica 48, (1998), 257-266.
• [12] J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Math. 1034, Springer-Verlag, 1983.
• [13] J. Musielak, On nonlinear integral operators, Atti Sem. Mat. Fis. Univ. Modena 47, (1999), 183-190.
• [14] M. Väth, Approximation, complete continuity and uniform measurability of Urysohn operators on general measure spaces, Nonlinear Analysis, 33 (1998), 715-728.
• [15] M. Väth, Volterra and Integral Equations of Vector Function, Marcel Dekker, New York, Basel, 2000.