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A combination of some weighted energy estimates is applied for the Cauchy problem of quasilinear wave equations with the standard null conditions in three spatial dimensions. Alternative proofs for global solutions are shown including the…

In this paper, we show the numerical solution for spherically symmetric SU(2) EinsteinYang-Mills (EYM) equations. We show the existence of entropy weak solution for EYM.

We define the universal exponential extension of an algebraically closed differential field and investigate its properties in the presence of a nice valuation and in connection with linear differential equations. Next we prove normalization…

In this paper we mainly investigate the Cauchy problem of a generalized Camassa-Holm equation. First by this relationship between the Degasperis-Procesi equation and the generalized Camassa-Holm equation, we then obtain two global…

This paper concerns a fully nonlinear version of the Yamabe problem on manifolds with boundary. We establish some existence results and estimates of solutions.

We construct Delaunay-type solutions for the fractional Yamabe problem with an isolated singularity $(-\Delta)^\gamma w = c_{n, \gamma} w^{\frac{n+2\gamma}{n-2\gamma}}, w>0 \ \mbox{in} \ \mathbb{R}^n \backslash \{0\}$ We follow a…

We derive a new generalization of the nonlinear variational wave equation. We prove existence of local, smooth solutions for this system. As a limiting case, we recover the nonlinear variational wave equation.

By using the global deformation of almost complex structures which are compatible with a symplectic form off a Lebesgue measure zero subset, we construct a (measurable) Lipschitz Kahler metric such that the one-form type Calabi-Yau equation…

The solution of symmetry equation of Yang-Mills self dual system is found in explicit form of its raising Hamiltonian operator. Thus explicit form of equations of self dual Yang Mills hierarchy is constructed.

We discuss the asymptotic form of the static axially symmetric, globally regular and black hole solutions, obtained recently in Einstein-Yang-Mills and Einstein-Yang-Mills-dilaton theory.

We generalize Jacod's condition and introduce a new type sufficient condition for the uniform integrability of the general stochastic exponential.

In the setting of Donaldson's conjecture on the Calabi-Yau equation on symplectic 4-manifolds, we prove an a priori estimate which in the K\"ahler case resembles a classical estimate of Cheng-Yau.

We extend the classical Landesman-Lazer results to the setting of second order Hamilton-Jacobi-Bellman equations. A number of new phenomena appear.

Via descent equations we derive formulas for consistent gauge anomalies in noncommutative Yang-Mills theories.

In this paper we study the Cauchy problem for the Landau Hamiltonian wave equation, with time dependent irregular (distributional) electromagnetic field and similarly irregular velocity. For such equations, we describe the notion of a `very…

We prove some new results related to Tanaka's formula.

Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…

Building on work of Du, Gao, and Yau, we give a characterization of smooth solutions, up to normalization, of the complex Plateau problem for strongly pseudoconvex Calabi--Yau CR manifolds of dimension $2n-1 \ge 5$ and in the hypersurface…

The aim of this paper is to solve a uniform version of the Yau-Tian-Donaldson conjecture for polarized toric manifolds. Also, we show a combinatorial sufficient condition for uniform relative K-polystability.

In the first part of this article, we will prove an existence-uniqueness result for generalized solutions of a mixed problem for linear hyperbolic system in the Colombeau algebra. In the second part, we apply this result to a wave…