We consider a forced differential difference equation and by the use of Laplace Transform Theory generate non-hypergeometric type series which we prove may be expressed in closed form.

Searching minimizers of functions on the convenient level set of the constrain function we obtain weak solutions of a non-homogenuous p-Laplace equation in border case without using the regularity results of linear elliptic equations .

We propose a new efficient and accurate numerical method based on harmonic polynomials to solve boundary value problems governed by 3D Laplace equation. The computational domain is discretized by overlapping cells. Within each cell, the velocity potential is represented by the linear superposition of a complete set of harmonic polynomials, which are the elementary solutions of Laplace equation....

A Carleman function is a special fundamental solution with a large parameter for the Laplace operator and gives a formula to calculate the value of the solution of the Cauchy problem in a domain for the Laplace equation. The probe method applied to an inverse boundary value problem for the Laplace equation in a bounded domain is based on the existence of a special sequence of harmonic functions...

This paper presents a mixed basis approach for Laplace eigenvalue problems, which treats the boundary as a perturbation of the free Laplace operator. The method separates the boundary from the volume via a generic function that can be pre-calculated and thereby effectively reduces the complexity of the problem to a calculation over the surface. Several eigenvalues are retrieved simultaneously. ...

The spectrum and the eigenbasis of the Laplace–Beltrami operator on the suspensions of toric automorphisms are investigated. A description in terms of solutions of one-dimensional Schrödinger’s equation is presented. Bibliography: 10 titles. §

In this note we prove the nonexistence of stable solutions to the p-Laplace equation −∆pu = eu on the entire Euclidean space RN , where p > 2 and N < p(p+3) p−1 .

The Laplace sequence of the discrete conjugate nets is constructed. The invariants of the nets satisfy, in full analogy to the continuous case, the system of difference equations equivalent to the discrete version of the generalized Toda equation.

We prove optimal integrability results for solutions of the p(·)-Laplace equation in the scale of (weak) Lebesgue spaces. To obtain this, we show that variable exponent Riesz and Wolff potentials map L to variable exponent weak Lebesgue spaces.

In this paper, we consider linear space-time fractional reactiondiffusion equation with composite fractional derivative as time derivative and Riesz-Feller fractional derivative with skewness zero as space derivative. We apply Laplace and Fourier transforms to obtain its solution.