Related papers: An evolutionary vector-valued variational inequali…

Homogenization is studied for a nonlinear elliptic boundary-value problem with a large nonlinear potential. More specifically we are interested in the asymptotic behavior of a sequence of p-Laplacians of the form $$…

We give a general Lagrange multiplier rule for mathematical programming problems in a Hausdorff locally convex space. We consider infinitely many inequality and equality constraints. Our results gives in particular a generalisation of the…

We consider the bifurcation problem $u'' + \lambda u = N(u)$ with two point boundary conditions where $N(u)$ is a general nonlinear term which may also depend on the eigenvalue $\lambda$. We give a variational characterization of the…

In this paper we establish existence, uniqueness, and boundedness results for an elliptic variational inequality coupled with a nonlinear ordinary differential equation. Under the general framework, we present a new application modelling…

We use a new variational method --based on the theory of anti-selfdual Lagrangians developed in [2] and [3]-- to establish the existence of solutions of convex Hamiltonian systems that connect two given Lagrangian submanifolds in $\R^{2N}$.…

Variational principles are important in the investigation of large classes of physical systems. They can be used both as analytical methods as well as starting points for the formulation of powerful computational techniques such as…

For some involutive maps $\Phi:{\mathbb C}P^1 \times {\mathbb C}P^1 \to {\mathbb C}P^1 \times {\mathbb C}P^1$ we find all invariants with separated variables. We investigate a link of the maps and their invariants with separated variables…

In this article, we prove existence and uniqueness of the Barenblatt solution of the evolution equation on the whole Euclidean space where the principle part is the nonlocal fractional p-Laplacian composed with a power function. Our proof…

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to…

This study investigates Dirichlet boundary condition related to a class of nonlinear parabolic problem with nonnegative $L^1$-data, which has a variable-order fractional $p$-Laplacian operator. The existence and uniqueness of renormalized…

Let $\tau$ denote the divisor function, and $f$ be any multiplicative function that satisfies some mild hypotheses. We establish the asymptotic formula or non-trivial upper bound for the shifted convolution sum $\sum_{n \leq…

New third- and fourth-order Lagrangian hierarchies are derived in this paper. The free coefficients in the leading terms satisfy the most general differential geometric criteria currently known for the existence of a variational…

We prove that a single-jump quantum stochastic unitary evolution is equivalent to a Dirac boundary value problem on the half line in an extra dimension. This amounts to the equivalence of the quantum measurement boundary-value problem in…

We consider variational inequality solutions with prescribed gradient constraints for first order linear boundary value problems. For operators with coefficients only in $L^2$, we show the existence and uniqueness of the solution by using a…

We extend classical results on variational inequalities with convex sets with gradient constraint to a new class of fractional partial differential equations in a bounded domain with constraint on the distributional Riesz fractional…

We consider solving equality-constrained nonlinear, nonconvex optimization problems. This class of problems appears widely in a variety of applications in machine learning and engineering, ranging from constrained deep neural networks, to…

An alternative class of the Lagrangian called the multiplicative form is suc- cessfully derived for a system with one degree of freedom for both non-relativistic and relativistic cases. This new Lagrangian can be considered as a…

We consider the asymptotic profiles of the nonlinear parabolic flows $$(e^{u})_{t}= \La u+\lambda e^u$$ to show the geometric properties of the following elliptic nonlinear eigenvalue problems known as a Gelfand's problem: \begin{equation*}…

This article is concerned with the second boundary value problem of the Lagrangian mean curvature type equation arising from special Lagrangian geometry. By the parabolic method, we consider a fully nonlinear parabolic equation with oblique…

In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered…