Positive solutions to nonlinear singular second order boundary value problems

Volume 64 / 1996

Gabriele Bonanno Annales Polonici Mathematici 64 (1996), 237-251 DOI: 10.4064/ap-64-3-237-251

Abstract

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.

Authors

  • Gabriele Bonanno

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