相关论文: Multi-index Based Solution Theory to the $\Phi^4$ …

This paper establishes the existence of infinitely many solutions for nonlinear problems without any symmetry, achieving three major advances. First, in the setting of semilinear elliptic PDEs, we introduce a refined variational truncation…

The last decades saw growing interest across multiple disciplines in nonlinear phenomena described by partial differential equations (PDE). Integrability of such equations is tightly related with the Painleve property - solutions being free…

We give a motivation and gentle introduction into the regularity structure and model introduced by Otto, Sauer, Smith and Weber, which fall into the framework of Hairer, but have a greedier index set than the one given by trees. We do this…

This paper investigates the existence of solutions for a class of nonlinear higher-order dynamic equations subject to mixed boundary conditions. We consider boundary value problems in which the nonlinear reaction functions satisfy…

An efficient linear solver plays an important role while solving partial differential equations (PDEs) and partial integro-differential equations (PIDEs) type mathematical models. In most cases, the efficiency depends on the stability and…

The problem of late time instability in time domain integral equations for electromagnetics is longstanding. While several techniques have been suggested for addressing this problem, they either require impractically high degrees of freedom…

We prove that the real four-dimensional Euclidean noncommutative \phi^4-model is renormalisable to all orders in perturbation theory. Compared with the commutative case, the bare action of relevant and marginal couplings contains…

We establish several delay-independent criteria for the existence and stability of positive periodic solutions of n-dimensional nonautonomous functional differential equation by several fixed point theorems. Examples from positive and…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

We prove existence of infinitely many classical periodic solutions with periodic boundary conditions for a class of monotone semilinear wave equations. Our argument relies on some new estimates for the linear problem with periodic boundary…

Some interesting (periodic!) solutions of certain systems of $4$ nonlinear Ordinary Differential Equations $dx_{n}\left( t\right) /dt=P_{2}^{\left( n\right) }\left[ x_{m}\left( t\right) \right] /\left[ x_{1}\left( t\right) +x_{2}\left(…

In this paper we provide conditions to ensure the existence, for $e>0$ sufficiently small, of periodic solutions of given period $T>0$ in a prescribed domain $U$ for a class of singularly perturbed first order differential systems. Here…

We present a novel approach for the construction of basis functions to be employed in selective or adaptive h-refined finite element applications with arbitrary-level hanging node configurations. Our analysis is not restricted to…

This work deals with the existence of an almost periodic solution for certain kind of differential equations with generalized piecewise constant argument, almost periodic coefficients which are seen as a perturbation of a linear equation of…

This work develops a multiscale solution decomposition (MSD) method for nonlocal-in-time problems to separate a series of known terms with multiscale singularity from the original singular solution such that the remaining unknown part…

We present a numerical study of the nonlinear system of $\Phi^4_0 $ equations of motion. The solution is obtained iteratively, starting from a precise point-sequence of the appropriate Banach space, for small values of the coupling…

In this paper we apply for the first time a new method for multivariate equation solving which was developed in \cite{gh1}, \cite{gh2}, \cite{gh3} for complex root determination to the {\em real} case. Our main result concerns the problem…

The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…

In this paper, we study the following semilinear Schr\"odinger equation with periodic coefficient: $$-\triangle u +V(x)u=f(x,u), u\in H^{1}(\mathbb{R}^{N}).$$ The functional corresponding to this equation possesses strongly indefinite…

The Partial Integral Equation (PIE) framework was developed to computationally analyze linear Partial Differential Equations (PDEs) where the PDE is first converted to a PIE and then the analysis problem is solved by solving operator-valued…