Gennaro Infante

Nonzero solutions of Hammerstein integral equations with discontinuous kernels

Using the theory of fixed point index, we establish new results for the existence of nonzero solutions of integral equations of the form u(t)=∫Gk(t,s)f(s,u(s))ds, where G is a compact set in Rn and k changes sign, so positive solutions may not exist, f satisfies Caratheodory conditions and k may be discontinuous. We apply our results to prove the existence of nontrivial solutions of some nonlocal boundary value problems.

Multiple nonnegative solutions of systems with coupled nonlinear boundary conditions

Using the theory of fixed point index, we discuss the existence and multiplicity of non-negative solutions of a wide class of boundary value problems with coupled nonlinear boundary conditions. Our approach is fairly general and covers a variety of situations. We illustrate our theory in an example all the constants that occur in our theory.

Multiple non-negative solutions of systems with coupled nonlinear BCs

Using the theory of fixed point index, we discuss the existence and multiplicity of non-negative solutions of a wide class of boundary value problems with coupled nonlinear boundary conditions. Our approach is fairly general and covers a variety of situations. We illustrate our theory in an example all the constants that occur in our theory.

Nonlocal impulsive boundary value problems with solutions that change sign

We discuss the existence of nonzero solutions for some second order impulsive boundary value problem subject to nonlocal boundary conditions. Our conditions are quite general and include, as special cases, the well‐known multi‐point boundary conditions, studied by other authors. Our approach relies on the classical fixed point index for compact maps.

New results related to a conjecture of Manickam and Singhi

In 1988 Manickam and Singhi conjectured that for every positive integer d and every n>=4d, every set of n real numbers whose sum is non-negative contains at least (n-1d-1) subsets of size d whose sums are non-negative. In this paper we make use of Halls matching theorem in order to study some numbers related to this conjecture.

Positive solutions of some nonlocal boundary value problems

We establish the existence of positive solutions of some m-point boundary value problems under weaker assumptions than previously employed. In particular, we do not require all the parameters occurring in the boundary conditions to be positive. Our results allow more general behaviour for the nonlinear term than being either sub- or superlinear.

Nontrivial solutions of a nonlinear heat flow problem via Sperner’s Lemma

Abstract In this paper we investigate the existence of multiple nontrivial solutions of a nonlinear heat flow problem with nonlocal boundary conditions. Our approach relies on the properties of a vector field on the phase plane and utilizes Sperner’s Lemma, combined with the continuum property of the solutions funnel.

Nontrivial solutions of Hammerstein integral equations with reflections

Using the theory of fixed point index, we establish new results for the existence of nonzero solutions of Hammerstein integral equations with reflections. We apply our results to a first-order periodic boundary value problem with reflections.MSC:34K10, 34B15, 34K13.

Nonzero radial solutions for a class of elliptic systems with nonlocal BCs on annular domains

We provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of Hammerstein integral equations. Some of the criteria involve a comparison with the spectral radii of some associated linear operators. We apply our results to prove the existence of multiple nonzero radial solutions for some systems of elliptic boundary value problems subject to nonlocal boundary conditions. Our approach is topological and relies on the classical fixed point index. We present an example to illustrate our theory.

A positive fixed point theorem with applications to systems of Hammerstein integral equations

We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of positive solutions for systems of nonlinear Hammerstein integral equations. An example is also presented to show the applicability of our results.MSC: 47H10, 34B10, 34B18, 45G15, 47H30.