Sentence examples for in singular potentials from inspiring English sources

The main reason of interest in singular potentials relies in their criticality: they have the same homogeneity as the Laplacian and the critical Sobolev exponent and do not belong to the Kato class, hence they cannot be regarded as the lower order perturbation terms.

We consider the Dirichlet problem of semi-linear corner-degenerate elliptic equations with singular potentials in the subcritical case.

In this paper, we established some existence results for a class of biharmonic equations with singular potentials in whole space by employing the Morse theory and variational methods.

This paper deals with the existence and multiplicity of symmetric solutions for a weighted semilinear elliptic system with multiple critical Hardy-Sobolev exponents and singular potentials in (mathbb{R}^{N}).

In this work, a biharmonic elliptic system is investigated in (mathbb{R}^{N}), which involves singular potentials and multiple critical exponents.

The abstract framework to study singular perturbations with symmetries developed in the paper allows one to incorporate physically meaningful connections between singular potentials V and the corresponding self-adjoint realizations of A0+V.

These scalar elliptic equations related to singular potentials, together with the corresponding elliptic systems, arise naturally in a wide range of physical fields and various economical prototypes [9].

In most of these papers, the authors deal with the elliptic problems involving singular potentials and critical exponents.

However, for more singular potentials, there are counterexamples to uniqueness.

In this paper, we study a class of biharmonic equations with a singular potential in (mathbb{R}^{N}).

In this paper, we investigated the existence of weak solutions for a two-dimensional Schrödinger equations with a singular potential in (mathbb{C}_).