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Positive solutions to nonlinear singular second order boundary value problems

Gabriele Bonanno — 1996

Annales Polonici Mathematici

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...

Two theorems on the Scorza Dragoni property for multifunctions

Gabriele Bonanno — 1989

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We point out two theorems on the Scorza Dragoni property for multifunctions. As an application, in particular, we improve a Carathéodory selection theorem by A. Cellina [4], by removing a compactness assumption.

Two theorems on the Scorza Dragoni property for multifunctions

Gabriele Bonanno — 1989

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

We point out two theorems on the Scorza Dragoni property for multifunctions. As an application, in particular, we improve a Carathéodory selection theorem by A. Cellina [4], by removing a compactness assumption.

An existence theorem of positive solutions to a singular nonlinear boundary value problem

Gabriele Bonanno — 1995

Commentationes Mathematicae Universitatis Carolinae

In this note we consider the boundary value problem y ' ' = f ( x , y , y ' ) ( x [ 0 , X ] ; X > 0 ) , y ( 0 ) = 0 , y ( X ) = a > 0 ; where f is a real function which may be singular at y = 0 . We prove an existence theorem of positive solutions to the previous problem, under different hypotheses of Theorem 2 of L.E. Bobisud [J. Math. Anal. Appl. 173 (1993), 69–83], that extends and improves Theorem 3.2 of D. O’Regan [J. Differential Equations 84 (1990), 228–251].

Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket

Gabriele BonannoGiovanni Molica BisciVicenţiu Rădulescu — 2012

ESAIM: Control, Optimisation and Calculus of Variations

Under an appropriate oscillating behaviour either at zero or at infinity of the nonlinear term, the existence of a sequence of weak solutions for an eigenvalue Dirichlet problem on the Sierpiński gasket is proved. Our approach is based on variational methods and on some analytic and geometrical properties of the Sierpiński fractal. The abstract results are illustrated by explicit examples.

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