Positive solutions of initial value problems for singular integro-differential equations in Banach space

• Autorzy: Liu Y. , Qi A.
• Języki publikacji: EN

Abstrakty

EN

Global existence of positive solutions on [0,1] are established in Banach space for singular initial value problems of first order integro-differential equation of the form x'(t) = f(t, x(t), (Tx)(t)), t € (0,1), [ x(0) = 0, where f(t,x,y) can be singular at t = 0,1 and x = 0. Some applications for second order singular initial or boundary value problems are worked out.

Słowa kluczowe

EN

positive solution; cone; singular initial value problem

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 4
• Strony: 847--858
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Liu Y.

• Department of Mathematics, Shandong Normal University, Jinan 250014, P.R.China

autor

Qi A.

• Department of Mathematics, Binzhou Medical College, Binzhou 256603, P.R.China

Bibliografia

• [1] V. Lakshmikantham, S. Leela, Nonlinear Differential Equations in Abstract Spaces, Pergamon, Oxford, 1981.
• [2] Dajun Guo, Jingxian Sun, Ordinary Differential Equations in Abstract Spaces, Shandong Science and Technology Publishing House, Jinan, 1989 (in Chinese).
• [3] Dajun Guo, V. Lakshmikantham, Xinzhi Liu, Nonlinear Integral Equations in Abstract Spaces, Kluwer Academic Publishers, Dordrecht, 1996.
• [4] R. P. Agarwal, D. O'Regan, Singular boundary value problems, Nonl. Anal. 27 (1996), 645-656.
• [5] R. P. Agarwal, D. O'Regan, Nonlinear superlinear and nonsingular second order boundary value problems, J. Differential Equations 143 (1998), 60-95.
• [6] R. P. Agarwal, D. O'Regan, Second-order boundary value problems of singular type, J. Math. Anal. Appl. 226 (1998), 414-430.
• [7] Wang Hongzhou, Deng Lihu and Ge Weigao, Positive solutions for a class of singular boundary value problem, Acta Math. Sini. 43 (2000), 385-390 (in Chinese).
• [8] V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, Vol. I-II, Acadamic Press, New York, 1969.