Related papers: Analytic solutions of nonlinear elliptic equations…

We prove new results on the existence, non-existence, localization and multiplicity of nontrivial radial solutions of a system of elliptic boundary value problems on exterior domains subject to nonlocal, nonlinear, functional boundary…

In this paper, we prove the long time stability of KAM tori for the nonlinear Schr\"odinger equation on the torus with arbitrary dimensions.

It is well recognized that new types of exact travelling wave solutions to nonlinear partial differential equations can be obtained by modifications of the methods which are in hand. In this study, we extend the class of auxiliary equations…

In this paper, we study a class of semilinear nonlocal elliptic equations posed on settings without compact Sobolev embedding. More precisely, we prove the existence of infinitely many solutions to the fractional Brezis-Nirenberg problems…

In this paper, we prove the existence of full dimensional invariant tori for a non-autonomous, almost-periodically forced nonlinear beam equation with a periodic boundary condition via KAM theory.

In the framework of the nonsmooth critical point theory for lower semi-continuous functionals, we propose a direct variational approach to investigate the existence of infinitely many weak solutions for a class of semi-linear elliptic…

We consider the numerical solution of nonlinear elliptic boundary value problems with Kansa's method. We derive analytic formulas for the Jacobian and Hessian of the resulting nonlinear collocation system and exploit them within the…

This note is devoted to some nonlocal, nonlinear elliptic problems with an emphasis on the computation of the solution of such problems, reducing it in particular to a fixed point argument in R. Errors estimates and numerical experiments…

In order to find analytically the travelling waves of partially integrable autonomous nonlinear partial differential equations, many methods have been proposed over the ages: "projective Riccati method", "tanh-method", "exponential method",…

The present work has two objectives. First, we prove that a weight\-ed superlinear elliptic problem has infinitely many nonradial solutions in the unit ball. Second, we obtain the same conclusion in annuli for a more general nonlinearity…

The family of fifth order nonlinear evolution equations is studied. Some traveling wave elliptic solutions are found. The classification of these exact solutions is given.

Solutions to most nonlinear ordinary differential equations (ODEs) rely on numerical solvers, but this gives little insight into the nature of the trajectories and is relatively expensive to compute. In this paper, we derive analytic…

We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on the Euclidean space and on compact Riemannian…

The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…

Ground state solutions of elliptic problems have been analyzed extensively in the theory of partial differential equations, as they represent fundamental spatial patterns in many model equations. While the results for scalar equations, as…

Exact solutions of some popular nonlinear ordinary differential equations are analyzed taking their Laurent series into account. Using the Laurent series for solutions of nonlinear ordinary differential equations we discuss the nature of…

In this article, we study an elliptic problem of mixed order with both local and nonlocal aspects involving singular nonlinearity in combination with critical Hartree-type nonlinearity. Using variational methods together with the critical…

Classical theory of Complex Multiplication (CM) shows that all abelian extensions of a complex quadratic field $K$ are generated by the values of appropriate modular functions at the points of finite order of elliptic curves whose…

The "noncommutative geometry" of complex algebraic curves is studied. As first step, we clarify a morphism between elliptic curves, or complex tori, and C*-algebras T_t={u,v | vu=exp(2\pi it)uv}, or noncommutative tori. The main result says…

Many nonlinear differential equations arising from practical problems may permit nontrivial multiple solutions relevant to applications, and these multiple solutions are helpful to deeply understand these practical problems and to improve…