Related papers: Quasilinearization Approach to Nonlinear Problems …
General solutions of nonlinear ordinary differential equations (ODEs) are in general difficult to find although powerful integrability techniques exist in the literature for this purpose. It has been shown that in some scalar cases…
We consider the existence and multiplicity of solutions for a class of quasi-linear Schr\"{o}dinger equations which include the modified nonlinear Schr\"{o}dinger equations. A new perturbation approach is used to treat the sub-cubic…
We develop a quasilinear theory of the Vlasov equation in order to describe the approach of systems with long-range interactions to quasi-stationary states. We derive a diffusion equation governing the evolution of the velocity distribution…
A class of fourth--order neutral type difference equations with quasidifferences and deviating arguments is considered. Our approach is based on studying the considered equation as a system of a four--dimensional difference system. The…
Carleman linearization is a technique that embeds systems of ordinary differential equations with polynomial nonlinearities into infinite dimensional linear systems in a procedural way. In this paper we generalize the method for systems of…
A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurence of higher-derivative…
A general method for solving nonlinear ill-posed problems is developed. The method consists of solving a Cauchy problem with a regularized operator and proving that the solution of this problem tends, as time grows, to a solution of the…
We show the existence of nontrivial solutions for a class of highly quasilinear problems in which the governing operators depend on the unknown function. By using a suitable variational setting and a weak version of the Cerami-Palais-Smale…
The method, proposed in the given work, allows the application of well developed standard methods used in quantum mechanics for approximate solution of the systems of ordinary linear differential equations with periodical coefficients.
We prove the existence and uniqueness of solution of the obstacle problem for quasilinear stochastic partial differential equations (OSPDEs for short) with Neumann boundary condition. Our method is based on the analytical technics coming…
Comparison principles are developed for discrete quasilinear elliptic partial differential equations. We consider the analysis of a class of nonmonotone Leray-Lions problems featuring both nonlinear solution and gradient dependence in the…
We generalize the classical K\"onig's and B\"ottcher's Theorems in complex dynamics to certain quasiregular mappings in the plane. Our approach to these results is unified in the sense that it does not depend on the local injectivity, or…
Whether integrable, partially integrable or nonintegrable, nonlinear partial differential equations (PDEs) can be handled from scratch with essentially the same toolbox, when one looks for analytic solutions in closed form. The basic tool…
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…
For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…
Numerical investigations of partial differential equations with hysteresis have largely focused on simulations, leaving numerical error analysis unexplored and relying mainly on derivative-free nonlinear solvers. This work establishes…
The purpose of this paper is to prove the existence of solutions of quasi-equilibrium problems without any generalized monotonicity assumption. Additionally, we give an application to quasi-optimization problems.
The Neumann--Neumann method is a commonly employed domain decomposition method for linear elliptic equations. However, the method exhibits slow convergence when applied to semilinear equations and does not seem to converge at all for…
This paper concerns the inclusion of Newton's method into an adaptive finite element method (FEM) for the solution of nonlinear partial differential equations (PDEs). It features an adaptive choice of the damping parameter in the Newton…