Existence of multiwavelets in $\mathbb {R}^n$

MULTIWAVELETS IN Rn WITH AN ARBITRARY DILATION MATRIX

We present an outline of how the ideas of self-similarity can be applied to wavelet theory, especially in connection to wavelets associated with a multiresolution analysis of R n allowing arbitrary dilation matrices and no restrictions on the number of scaling functions. 1. Introduction Wavelet bases have proved highly useful in many areas of mathematics, science, and engineering. One of the mo...

Existence of a ground state solution for a class of singular elliptic problem in RN$\mathbb{R}^{N}$

when p = , |f (x,u)| ≤ c(|u|+ |u|q–),  < q≤ ∗ = N N– ,N ≥ , for the corresponding results onemay refer to Brézis [], Brézis and Nirenberg [], Bartsch andWillem [] and Capozzi, Fortunato and Palmieri []. Garcia and Alonso [] generalized Brézis, Nirenberg’s existence and nonexistence results to p-Laplace equation. Moreover, let us consider the following semilinear Schrödinger equation:

Existence of nontrivial solutions for a class of biharmonic equations with singular potential in RN$\mathbb{R}^{N}$

*Correspondence: [email protected] School of Mathematics and Physics, University of South China, Hengyang, P.R. China Abstract In this paper, we study a class of biharmonic equations with a singular potential inRN . Under appropriate assumptions on the nonlinearity, we establish some existence results via the Morse theory and variational methods. We significantly extend and complement some re...

Positive solutions for coupled Schrödinger system with critical exponent in RN$\mathbb{R}^{N}$ (N≥5$N\geq5$)

EXISTENCE OF POSITIVE SOLUTIONS FOR NONLINEAR BOUNDARY VALUE PROBLEMS IN BOUNDED DOMAINS OF Rn

Let D be a bounded domain in Rn (n ≥ 2). We consider the following nonlinear elliptic problem: Δu = f (·,u) in D (in the sense of distributions), u|∂D = φ, where φ is a nonnegative continuous function on ∂D and f is a nonnegative function satisfying some appropriate conditions related to some Kato class of functions K(D). Our aim is to prove that the above problem has a continuous positive solu...