Related papers: Gap in Nonlinear Equivalence for Numerical Methods…
The Monotonicity inequality is an important tool in the understanding of existence and uniqueness of strong solutions for Stochastic PDEs. In this article, we discuss three approaches to establish this deterministic inequality explicitly.
In this paper we consider the stability and convergence of numerical discretizations of the Black-Scholes partial differential equation (PDE) when complemented with the popular linear boundary condition. This condition states that the…
Selection of 25 examples from extensive nontrivial families for different types of nonlinear PDEs and their formal general solutions are given. The main goal here is to show on examples the types of solvable PDEs and what their general…
This paper presents new analytical results for a class of nonlinear parabolic systems of partial different equations with small cross-diffusion which describe the macroscopic dynamics of a variety of large systems of interacting particles.…
The Bohl-Perron result on exponential dichotomy for a linear difference equation $$ x(n+1)-x(n) + \sum_{l=1}^m a_l(n)x(h_l(n))=0, h_l(n)\leq n, $$ states (under some natural conditions) that if all solutions of the non-homogeneous equation…
We consider abstract evolution equations with a nonlinear term depending on the state and on delayed states. We show that, if the $C_0$-semigroup describing the linear part of the model is exponentially stable, then the whole system retains…
Existence and non-existence results are established for quasilinear elliptic problems with nonlinear boundary conditions and lack of compactness. The proofs combine variational methods with the geometrical feature, due to the competition…
We apply geometric techniques to obtain the necessary and sufficient conditions on the existence and nonlinear stability of self-gravitating Riemann ellipsoids having at least two equal axes.
A simple trick is illustrated, whereby nonlinear evolution equations can be modified so that they feature a lot - or, in some cases, only -- periodic solutions. Several examples (ODEs and PDEs) are exhibited.
This paper concerns the stability of analytical and numerical solutions of nonlinear stochastic delay differential equations (SDDEs). We derive sufficient conditions for the stability, contractivity and asymptotic contractivity in mean…
The present article considers stability of the solutions to nonlinear and nonautonomous compartmental systems governed by ordinary differential equations (ODEs). In particular, compartmental systems with a right-hand side that can be…
We study the stabilization and the wellposedness of solutions of the wave equation with subcritical semilinearities and locally distributed nonlinear dissipation. The novelty of this paper is that we deal with the difficulty that the main…
We consider the nonlinear Neumann problem for fully nonlinear elliptic PDEs on a quadrant. We establish a comparison theorem for viscosity sub and supersolutions of the nonlinear Neumann problem. The crucial argument in the proof of the…
We consider a specific type of nonlinear partial differential equations (PDE) that appear in mathematical finance as the result of solving some optimization problems. We review some existing in the literature examples of such problems, and…
A method for the study of steady-state nonlinear modes for Gross-Pitaevskii equation (GPE) is described. It is based on exact statement about coding of the steady-state solutions of GPE which vanish as $x\to+\infty$ by reals. This allows to…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion. In particular, spaces of generalized functions are constructed that contain generalized solutions to all systems of continuous,…
We prove a comparison result for viscosity solutions of (possibly degenerate) parabolic fully nonlinear path-dependent PDEs. In contrast with the previous result in Ekren, Touzi & Zhang, our conditions are easier to check and allow for the…
A quadratic inequality is formulated in the paper. An estimate on the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations.
In present paper, we establish sufficient conditions for existence and stability of solutions for system of nonlinear implicit fractional differential equations. The main techniques are based on method of successive approximations. Finally,…