Alberto Boscaggin

Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case

We study the periodic and the Neumann boundary value problems associated with the second order nonlinear differential equation begin{equation*} u + c u + lambda a(t) g(u) = 0, end{equation*} where

Monotone twist maps and periodic solutions of systems of Duffing type

g colon mathopen{[}0,+inftymathclose{[}to mathopen{[}0,+inftymathclose{[}

Multiple positive solutions to elliptic boundary blow-up problems

is a sublinear function at infinity having superlinear growth at zero. We prove the existence of two positive solutions when

Scattering Parabolic Solutions for the Spatial N-Centre Problem

int_{0}^{T} a(t) !dt 0

Periodic solutions of a perturbed Kepler problem in the plane: From existence to stability

is sufficiently large. Our approach is based on Mawhins coincidence degree theory and index computations.

Asymptotic and chaotic solutions of a singularly perturbed Nagumo-type equation

The theory of twist maps is applied to prove the existence of many harmonic and sub-harmonic solutions for certain Newtonian systems of differential equations. The method of proof leads to very precise information on the oscillatory properties of these solutions.

Periodic solutions and regularization of a Kepler problem with time-dependent perturbation

Abstract We prove the existence of multiple positive radial solutions to the sign-indefinite elliptic boundary blow-up problem { Δ u + ( a + ( | x | ) − μ a − ( | x | ) ) g ( u ) = 0 , | x | 1 , u ( x ) → ∞ , | x | → 1 , where g is a function superlinear at zero and at infinity, a + and a − are the positive/negative part, respectively, of a sign-changing function a and μ > 0 is a large parameter. In particular, we show how the number of solutions is affected by the nodal behavior of the weight function a . The proof is based on a careful shooting-type argument for the equivalent singular ODE problem. As a further application of this technique, the existence of multiple positive radial homoclinic solutions to Δ u + ( a + ( | x | ) − μ a − ( | x | ) ) g ( u ) = 0 , x ∈ R N , is also considered.

Positive subharmonic solutions to nonlinear ODEs with indefinite weight

AbstractFor the N-centre problem in the three dimensional space,n

Parabolic solutions for the planar N-centre problem: multiplicity and scattering

{ddot{x}} = -sum_{i=1}^{N}nfrac{m_i ,(x-c_i)}{vert x - c_i vert^{alpha+2}}, qquad x in {mathbb{R}}^3 {setminus}n{c_1,ldots,c_N},