Positive solutions to nonlinear singular second order boundary value problems

• Autorzy: Gabriele Bonanno
• Języki publikacji: EN

Abstrakty

EN

Existence theorems of positive solutions to a class of singular second order boundary value problems of the form y'' + f(x,y,y') = 0, 0 < x < 1, are established. It is not required that the function (x,y,z) → f(x,y,z) be nonincreasing in y and/or z, as is generally assumed. However, when (x,y,z) → f(x,y,z) is nonincreasing in y and z, some of O'Regan's results [J. Differential Equations 84 (1990), 228-251] are improved. The proofs of the main theorems are based on a fixed point theorem for weakly sequentially continuous operators.

Słowa kluczowe

EN

singular boundary value problem   positive solution  

Kategorie tematyczne

• 34B15: Nonlinear boundary value problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996
• Tom: 64
• Numer: 3
• Strony: 237-251

Daty

wydano

1996

otrzymano

1995-05-27

Twórcy

autor

Gabriele Bonanno

• Dipartimento di Ingegneria Elettronica e Matematica Applicata, Università di Reggio Calabria, via E. Cuzzocrea 48, 89128 Reggio Calabria, Italy

Bibliografia

• [1] O. Arino, S. Gautier and J. P. Penot, A fixed point theorem for sequentially continuous mappings with application to ordinary differential equations, Funkcial. Ekvac. 27 (1984), 273-279.
• [2] L. E. Bobisud, Existence of positive solutions to some nonlinear singular boundary value problems on finite and infinite intervals, J. Math. Anal. Appl. 173 (1993), 69-83.
• [3] L. E. Bobisud, D. O'Regan and W. D. Royalty, Solvability of some nonlinear boundary value problems, Nonlinear Anal. 12 (1988), 855-869.
• [4] G. Bonanno, An existence theorem of positive solutions to a singular nonlinear boundary value problem, Comment. Math. Univ. Carolin. 36 (1995), 609-614.
• [5] A. Callegari and A. Nachman, Some singular, nonlinear differential equations arising in boundary layer theory, J. Math. Anal. Appl. 64 (1978), 96-105.
• [6] J. Diestel and J. J. Uhl, Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., 1977.
• [7] J. A. Gatica, V. Oliker and P. Waltman, Singular nonlinear boundary value problems for second-order ordinary differential equations, J. Differential Equations 79 (1989), 62-78.
• [8] A. Nachman and A. Callegari, A nonlinear singular boundary value problem in theory of pseudoplastic fluids, SIAM J. Appl. Math. 38 (1980), 275-281.
• [9] D. O'Regan, Positive solutions to singular and nonsingular second order boundary value problems, J. Math. Anal. Appl. 142 (1989), 40-52.
• [10] D. O'Regan, Existence of positive solutions to some singular and nonsingular second order boundary value problems, J. Differential Equations 84 (1990), 228-251.
• [11] S. D. Taliaferro, A nonlinear singular boundary value problem, Nonlinear Anal. 3 (1979), 897-904.