Related papers: On solutions to Walcher's extended holomorphic ano…

We obtain special solutions of the $q$-Heun equation which are expressed as finite summations of $q$-hypergeometric functions. These solutions are obtained by considering the $q$-integral transformations of the polynomial-type solutions.

In this paper we establish existence and compactness of solutions to a general fully nonlinear version of the Yamabe problem on locally conformally flat Riemannian manifolds with umbilic boundary.

In this paper, we define a parametric variant of generalized Euler sums and call them the (alternating) parametric Euler $T$-sums. By using the contour integration method and residue theorem, we establish several explicit formulae for the…

In work the numerical solutions of Kundu-Eckhaus equation are presented. The conditions of dominate nonlinearity or disperse are cleared up.

The solutions of the Landau-Lifshitz equation with finite-gap behavior at infinity are considered. By means of the inverse scattering method the large-time asymptotics is obtained.

We estabish an analog of the Cauchy-Poincare separation theorem for normal matrices in terms of majorization. Moreover, we present a solution to the inverse spectral problem (Borg-type result) for a normal matrix. Using this result we…

In this paper, we introduce a novel identity for generalized Euler polynomials, leading to further generalizations for several relations involving classical Euler numbers, Euler polynomials, Genocchi polynomials, and Genocchi numbers.

We survey the various constructions of forward self-similar solutions (and generalizations of self-similar solutions) to the Navier-Stokes equations. We also include and prove an extension of a recent result from [7].

Let $\Omega\subseteq \mathbb{R}^N$ a bounded open set, $N\geq 2$, and let $p>1$; we prove existence of a renormalized solution for parabolic problems whose model is $$ \begin{cases} u_{t}-\Delta_{p} u=\mu & \text{in}\…

An extension of the Wigner-Araki-Yanase theorem to multiplicative conserved quantities is presented and approximate versions of the theorem are discussed.

One discovers why the solution of generalized umbral calculus difference nonhomogeneous equation in the form recently proposed by the author extends here now to generalized appellian delta operator and corresponding polynomials case almost…

We introduce new hypergeometric series expansions of the solutions to the general Heun equation. The form of the Gauss hypergeometric functions used as expansion function differs from that used before. We derive three such expansions and…

We present a simple method to obtain vacuum solutions of Einstein's equations in parabolic coordinates starting from ones with cylindrical symmetries. Furthermore, a generalization of the method to a more general situation is given together…

We provide a complete study of existence and uniqueness of solutions to the Lichnerowicz equation in general relativity with arbitrary mean curvature.

This paper is concerned with the final value problem for a system of nonlinear wave equations. The main issue is to solve the problem for the case where the nonlinearity is of a long range type. By assuming that the solution is spherically…

We continue here with previous investigations on the global behavior of general type non-linear wave equations for a class of small, scale-invariant initial data. The method is based on the use of a new set of Strichartz estimates for the…

We prove an infinitary version of the Brauer-Schur theorem.

wave solutions to nonlinear partial differential equations. We simplify the so called (G'/G)-expansion method and apply two of those methods to simple physical problems.

The Cauchy problem for the inhomogeneous Helmholtz equation with non-uniform refraction index is considered. The ill-posedness of this problem is tackled by means of the variational form of mollification. This approach is proved to be…

The Anomaly flow is shown to converge on toric fibrations with the Fu-Yau ansatz, for both positive and negative values of the slope parameter $\alpha'$. This implies both results of Fu and Yau on the existence of solutions for…