Paolamaria Pietramala

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.

Convergence of approximating fixed points sets for multivalued nonexpansive mappings

Let K be a closed convex subset of a Hilbert space H and T:K —o K a nonexpansive multivalued map with a unique fixed point z such that {z} = T(z). It is shown that we can construct a sequence of approxi mating fixed point sets converging in the sense of Mosco to z.

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.

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.

Solutions of perturbed Hammerstein integral equations with applications

Abstract By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical results, we study some problems that occur in applied mathematics, namely models of chemical reactors, beams and thermostats. We also apply our theory in order to prove the existence of nontrivial radial solutions of systems of elliptic boundary value problems subject to nonlocal, nonlinear boundary conditions.

Non-trivial solutions of local and non-local Neumann boundary-value problems

We prove new results on the existence, non-existence, localization and multiplicity of non-trivial solutions for perturbed Hammerstein integral equations. Our approach is topological and relies on the classical fixed-point index. Some of the criteria involve a comparison with the spectral radius of some related linear operators. We apply our results to some boundary-value problems with local and non-local boundary conditions of Neumann type. We illustrate in some examples the methodologies used.

Existence Results for Impulsive Systems with Initial Nonlocal Conditions

AbstractWe study the existence of solutions for nonlinear first order impulsive systems with nonlocal initial conditions. Our approach relies in the fixed point principles of Schauder and Perov, combined with a vector approach that uses matrices that converge to zero. We prove existence and uniqueness results for these systems. Some examples are presented to illustrate the theory.

Nonnegative solutions for a system of impulsive BVPs with nonlinear nonlocal BCs

We study the existence of nonnegative solutions for a system of impulsive differential equations subject to nonlinear, nonlocal boundary conditions. The system presents a coupling in the differential equation and in the boundary conditions. The main tool that we use is the theory of fixed point index for compact maps. u 00 (t) +g1(t)f1 t;u(t);v(t) = 0; t2 (0; 1); t6 1; v 00 (t) +g2(t)f2 t;u(t);v(t) = 0; t2 (0; 1); t6 2;