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Multiplicity solutions of a class fractional Schrödinger equations

100%

Jia L.-J., Ge B., Cui Y.-X., Sun L.-L.

Open Mathematics

2017

tom 15

nr 1

1010-1023

In this paper, we study the existence of nontrivial solutions to a class fractional Schrödinger equations (−Δ)su+V(x)u=λf(x,u)inRN, $$ {( - \Delta )^s}u + V(x)u = \lambda f(x,u)\,\,{\rm in}\,\,{\mathbb{R}^N}, $$ where [...] (−Δ)su(x)=2limε→0∫RN∖Bε(X)u(x)−u(y)|x−y|N+2sdy,x∈RN $ {( - \Delta )^s}u(x) = 2\lim\limits_{\varepsilon \to 0} \int_ {{\mathbb{R}^N}\backslash {B_\varepsilon }(X)} {{u(x) - u(y)} \over {|x - y{|^{N + 2s}}}}dy,\,\,x \in {\mathbb{R}^N} $ is a fractional operator and s ∈ (0, 1). By using variational methods, we prove this problem has at least two nontrivial solutions in a suitable weighted fractional Sobolev space.

A spectral estimate for the Dirac operator on Riemannian flows

84%

Ginoux N., Habib G.

Open Mathematics

2010

tom 8

nr 5

950-965

We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We derive an estimate on both Sasakian and 3-dimensional manifolds, and partially classify those satisfying the limiting case. Finally, we compare our estimate with a lower bound in terms of a natural tensor depending on the eigenspinor.

Ograniczanie wyników

2 Open Mathematics

1 Cui Y.-X.

1 Ge B.

1 Ginoux N.

1 Habib G.

1 Jia L.-J.

1 Sun L.-L.

1 2017

1 2010

Wyniki wyszukiwania

Multiplicity solutions of a class fractional Schrödinger equations

A spectral estimate for the Dirac operator on Riemannian flows