Related papers: A variational method for functionals depending on …
Let $M$ be an $n$-dimensional closed Riemannian manifold with metric $g$, $d\mu=e^{-\phi(x)}d\nu$ be the weighted measure and $\Delta_{p,\phi}$ be the weighted $p$-Laplacian. In this article we will investigate monotonicity for the first…
We use discrete holomorphic polynomials to prove that, given a refining sequence of critical maps of a Riemann surface, any holomorphic function can be approximated by a converging sequence of discrete holomorphic functions.
In this short survey, we derive some weyl-type universal inequalities of eigenvalues of the Laplacian on a closed Riemannian manifold of nonnegative Ricci curvature. We also give upper bounds for the $L_{\infty}$ norm of eigenfunctions of…
The formalism of Supersymmetric Quantum Mechanics provides us the eigenfunctions to be used in the variational mathod to obtain the eigenvalues for the Hulth\'en Potential.
This article shows that counting or computing the small eigenvalues of the Witten Laplacian in the semi-classical limit can be done without assuming that the potential is a Morse function as the authors did in [LNV]. In connection with…
In this paper, we investigate eigenvalues of the Dirichlet problem and the closed eigenvalue problem of drifting Laplacian on the complete metric measure spaces and establish the corresponding general formulas. By using those general…
We study Yamabe-type equations on the product of two spheres $(S^n \times S^n, G_\delta)$, where $G_\delta$ is a family of Riemannian metrics parametrized by $\delta > 0$. Using bifurcation theory and isoparametric functions, we establish…
This study introduces a novel spatial autoregressive model in which the dependent variable is a function that may exhibit functional autocorrelation with the outcome functions of nearby units. This model can be characterized as a…
The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…
This work investigates a new approach to find closed form analytical approximate solution of linear initial value problems. Classical Bernoulli polynomials have been used to derive a finite set of orthonormal polynomials and a finite…
To study and develop wall-functions for low-Reynolds-number models, a model linear equation is introduced. This equation simulates major mathematical peculiarities of the low-Reynolds-number model including a near wall sub-layer and…
We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Pad\'e approximation of the Laplace…
Let X=H\G be a homogeneous spherical variety for a split reductive group G over the integers o of a p-adic field k, and K=G(o) a hyperspecial maximal compact subgroup of G=G(k). We compute eigenfunctions ("spherical functions") on X=X(k)…
We present a new construction for obtaining pairs of higher-step isospectral Riemannian nilmanifolds and compare several resulting new examples. In particular, we present new examples of manifolds that are isospectral on functions, but not…
We investigate functionals defined on manifolds through parameterizations. If they are to be meaningful, from a geometrical viewpoint, they ought to be invariant under reparameterizations. Standard, local, integral functionals with this…
We propose a novel algorithmic method for constructing invariant variational schemes of systems of ordinary differential equations that are the Euler-Lagrange equations of a variational principle. The method is based on the invariantization…
In this paper we consider the functional whose critical points are solutions of the fractional CR Yamabe type equation on the sphere. We firstly study the behavior of the Palais-Smale sequences characterizing the bubbling phenomena and…
We consider in this paper an area functional defined on submanifolds of fixed degree immersed into a graded manifold equipped with a Riemannian metric. Since the expression of this area depends on the degree, not all variations are…
We calculate the least upper bounds of pointwise and uniform approximations for classes of $2\pi$-periodic functions expressible as convolutions of an arbitrary square summable kernel with functions, which belong to the unit ball of the…
We develop method that allows to derive reductions and solutions to hyperbolic systems of partial differential equations. The method is based on using functions that are constant in the direction of characteristics of the system. These…