Periodic solutions for a class of second-order Hamiltonian systems.
Multiplicity results for a perturbed elliptic Neumann problem.
Infinitely many solutions for a boundary value problem with discontinuous nonlinearities.
Positive solutions to nonlinear singular second order boundary value problems
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
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
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
In this note we consider the boundary value problem , , ; where is a real function which may be singular at . 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].
Existence of solutions for a multivalued boundary value problem with non-convex and unbounded right-hand side
Infinitely many solutions for a mixed boundary value problem
The existence of infinitely many solutions for a mixed boundary value problem is established. The approach is based on variational methods.
A characterization of the existence of solutions to some higher order boundary value problems
The aim of this short note is to present a theorem that characterizes the existence of solutions to a class of higher order boundary value problems. This result completely answers a question previously set by the authors in [Differential Integral Equations (1993), 1119–1123].
Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket
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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