Multiple normalized solutions for a Sobolev critical Schrödinger equation

Ja n 20 04 Schrödinger equation with critical Sobolev exponent

Bifurcation of Positive Solutions for a Semilinear Equation with Critical Sobolev Exponent

In this note we consider bifurcation of positive solutions to the semilinear elliptic boundary-value problem with critical Sobolev exponent −∆u = λu− αu + u −1, u > 0, in Ω, u = 0, on ∂Ω. where Ω ⊂ Rn, n ≥ 3 is a bounded C2-domain λ > λ1, 1 < p < 2∗ − 1 = n+2 n−2 and α > 0 is a bifurcation parameter. Brezis and Nirenberg [2] showed that a lower order (non-negative) perturbation can contribute t...

On Multiple Solutions for a Singular Quasilinear Elliptic System Involving Critical Hardy-sobolev Exponents

This paper is concerned with the existence of nontrivial solutions for a class of degenerate quasilinear elliptic systems involving critical Hardy-Sobolev type exponents. The lack of compactness is overcame by using the Brezis-Nirenberg approach, and the multiplicity result is obtained by combining a version of the Ekeland’s variational principle due to Mizoguchi with the Ambrosetti-Rabinowitz ...

Existence of Multiple Solutions for a Singular Elliptic Problem with Critical Sobolev Exponent

and Applied Analysis 3 The following Hardy-Sobolev inequality is due to Caffarelli et al. 12 , which is called Caffarelli-Kohn-Nirenberg inequality. There exist constants S1, S2 > 0 such that (∫ RN |x|−bp |u|pdx )p/p∗ ≤ S1 ∫ RN |x|−ap|∇u|pdx, ∀u ∈ C∞ 0 ( R N ) , 1.8 ∫ RN |x|− a 1 |u|dx ≤ S2 ∫ RN |x|−ap|∇u|pdx, ∀u ∈ C∞ 0 ( R N ) , 1.9 where p∗ Np/ N − pd is called the Sobolev critical exponent. ...

Investigation of analytical and numerical solutions for one-dimensional independent-oftime Schrödinger Equation

In this paper, the numerical solution methods of one- particale, one – dimensional time- independentSchrodinger equation are presented that allows one to obtain accurate bound state eigen values andeigen functions for an arbitrary potential energy function V(x). These methods included the FEM(Finite Element Method), Cooly, Numerov and others. Here we considered the Numerov method inmore details...