1,354,142 research outputs found
A global bifurcation result for a second order singular equation
No full textDedicated, with gratefulness and friendship, to Professor Fabio Zanolin on the occasion of his 60th birthday Abstract. We deal with a boundary value problem associated to a second order singular equation in the open interval (0, 1]. We first study the eigenvalue problem in the linear case and discuss the nodal properties of the eigenfunctions. We then give a global bifurcation result for nonlinear problems
Multiplicity results for systems of asymptotically linear second order equations
No full textWe prove the existence and multiplicity of solutions, with prescribed nodal properties, for a BVP associated with a system of asymptotically linear second order equations. The applicability of an abstract continuation theorem is ensured by upper and lower bounds on the number of zeros of each component of a solutio
A multiplicity result for a class of strongly indefinite asymptotically linear second order systems
No full textWe prove a multiplicity result for a class of strongly indefinite nonlinear second order asymptotically linear systems with Dirichlet boundary conditions. The key idea for the proof is to bring together the classical shooting method and the Maslov index of the linear Hamiltonian systems associated to the asymptotic limits of the given nonlinearit
Uniqueness in law for stochastic boundary value problems
No full textWe study existence and uniqueness of solutions for second order ordinary stochastic differential equations with Dirichlet boundary conditions on a given interval. In the first part of the paper we provide sufficient conditions to ensure pathwise uniqueness, extending some known results. In the second part we show sufficient conditions to have the weaker concept of uniqueness in law and provide a significant example. Such conditions involve a linearized equation and are of different type with respect to the ones which are usually imposed to study pathwise uniqueness. This seems to be the first paper which deals with uniqueness in law for (anticipating) stochastic boundary value problems. We mainly use functional analytic tools and some concepts of Malliavin Calculus
On the existence of two solutions with a prescribed number of zeros for a superlinear two-point boundary value problem
No full textNO ABSTRAC
Linear and nonlinear eigenvalue problems for Dirac systems in unbounded domains
No full textWe first study the linear eigenvalue problem for a planar Dirac system in the open half-line and describe the nodal properties of its solution by means of the rotation number. We then give a global bifurcation result for a planar nonlinear Dirac system in the open half-line. As an application,we provide a global continuum of solutions of the nonlinear Dirac equation which have a special form
Detecting multiplicity for systems of second order equations: an alternative approach
No full textIn this paper we are concerned with a system of second-order differential equations of the form x'' + A(t, x)x = 0, t ∈ [0, T], x ∈ R^N, where A(t, x) is a symmetric N × N matrix. We concentrate on an asymptotically linear situation and we prove the existence of multiple solutions to the Dirichlet problem associated to the system. Multiplicity is obtained by a comparison between the number of moments of verticality of the matrices which are the uniform limits of A(t, x) for |x| → 0 and |x| → +∞, respectively. For the proof, which is based on a generalized shooting approach, we provide a theorem on the existence of zeros of a class of N-dimensional vector fields
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