相关论文: Landesman-Lazer type results for second order Hami…

Recently the Hamilton-Jacobi formulation for first order constrained systems has been developed. In such formalism the equations of motion are written as total differential equations in many variables. We generalize the Hamilton-Jacobi…

We present multiplicity results for the periodic and Neumann-type boundary value problems associated with coupled Hamiltonian systems. For the periodic problem, we couple a system having twist condition with another one whose nonlinearity…

We discuss a general procedure for arriving at the Hamilton-Jacobi equation of second-class constrained systems, and illustrate it in terms of a number of examples by explicitely obtaining the respective Hamilton principal function, and…

We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics to higher order field theories with regular lagrangian density. We also investigate the dependence of the formalism on the lagrangian density in the class of those…

We study the existence and the properties of solutions to the Dirichlet problem for uniformly elliptic second-order Hamilton-Jacobi-Bellman operators, depending on the principal eigenvalues of the operator.

We prove explicit estimates for the error in random homogenization of degenerate, second-order Hamilton-Jacobi equations, assuming the coefficients satisfy a finite range of dependence. In particular, we obtain an algebraic rate of…

Trivial second-order Lagrangians are studied and a complete description of the dependence on the second-order derivatives is given. This extends previous work of Olver and others. In particular, this description involves some polynomial…

The method of parameter variation for linear differential equations is extended to classes of second order nonlinear differential equations. This allows to reduce the latter to first order differential equations. Known classical equations…

This paper deals with the Landesman-Lazer type problem of elliptic equations associated with homogeneous Dirichlet boundary conditions. By using some dynamical arguments we derive some new results on bifurcation from infinity and…

We investigate in this work a fully-discrete semi-Lagrangian approximation of second order possibly degenerate Hamilton-Jacobi-Bellman (HJB) equations on a bounded domain with oblique boundary conditions. These equations appear naturally in…

A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated…

We first highlight the main differences between second order and higher order linear parabolic equations. Then we survey existing results for the latter, in particular by analyzing the behavior of the convolution kernels. We illustrate the…

This paper addresses an investigation on a factorization method for difference equations. It is proved that some classes of second order linear difference operators, acting in Hilbert spaces, can be factorized using a pair of mutually…

We obtain space-time H\"older regularity estimates for solutions of first- and second-order Hamilton-Jacobi equations perturbed with an additive stochastic forcing term. The bounds depend only on the growth of the Hamiltonian in the…

We present comparison principles, Lipschitz estimates and study state constraints problems for degenerate, second-order Hamilton-Jacobi equations.

We derive the discrete version of the classical Helmholtz condition. Precisely, we state a theorem characterizing second order finite differences equations admitting a Lagrangian formulation. Moreover, in the affirmative case, we provide…

This work presents a newly renovated approach to the analysis of second-order Riccati equations from the point of view of the theory of Lie systems. We show that these equations can be mapped into Lie systems through certain Legendre…

We prove an extension of Hoermander's classical result on hypoelliptic second order equations, where the coefficients of the related vector fields are globally Lipschitz and satisfy the classical Hoermander condition on a dense set while…

We exhibit an alternative method for solving inhomogeneous second--order linear ordinary dynamic equations on time scales, based on reduction of order rather than variation of parameters. Our form extends recent (and long-standing) analysis…

This paper introduces a notion of viscosity solutions for second order elliptic Hamilton-Jacobi-Bellman (HJB) equations with infinite delay associated with infinite-horizon optimal control problems for stochastic differential equations with…