# On the bounds of the sum of eigenvalues for a Dirichlet problem involving mixed fractional Laplacians

@article{Chen2020OnTB, title={On the bounds of the sum of eigenvalues for a Dirichlet problem involving mixed fractional Laplacians}, author={Huyuan Chen and Mousomi Bhakta and Hichem Hajaiej}, journal={Journal of Differential Equations}, year={2020} }

## 8 Citations

### Normalized solutions for a class of scalar field equations involving mixed fractional Laplacians

- MathematicsAdvanced Nonlinear Studies
- 2022

Abstract The purpose of this article is to establish sharp conditions for the existence of normalized solutions to a class of scalar field equations involving mixed fractional Laplacians with…

### On the Dirichlet problem for fractional Laplace equation on a general domain

- Mathematics
- 2022

In this paper, we study the weak strong uniqueness of the Dirichlet type problems of fractional Laplace (Poisson) equations. We construct the Green’s function and the Poisson kernel. We then provide…

### Existence of Normalized Solutions and some Applications

- Mathematics
- 2022

We give an abstract framework to prove the existence of normalized solutions for a large class of PDEs. We will then exhibit some applications, where we show the existence of normalized solutions for…

### A sharp Gagliardo-Nirenberg inequality and its application to fractional problems with inhomogeneous nonlinearity

- MathematicsEvolution Equations and Control Theory
- 2022

The purpose of this paper is threefold. Firstly, we establish a Gagliardo-Nirenberg inequality with optimal constant, which involves a fractional norm and an inhomogeneous nonlinearity. Secondly, as…

### A General and Unified Method to prove the Uniqueness of Ground State Solutions and the Existence/Non-existence, and Multiplicity of Normalized Solutions with applications to various NLS

- Mathematics
- 2022

We first give an abstract framework to show the uniqueness of Ground State Solutions (GSS) for a large class of PDEs. To the best of our knowledge, all the existing results in the literature only…

### On the Eigenvalues of the $p\&q-$ Fractional Laplacian

- Mathematics
- 2023

We consider the eigenvalue problem for the fractional $p \&q-$Laplacian \begin{equation} \left\{\begin{aligned} (- \Delta)_p^{s}\, u + \mu(- \Delta)_q^{s}\, u+ |u|^{p-2}u+\mu|u|^{q-2}u=\lambda\…

### On the weighted Dirichlet eigenvalues of Hardy operators involving critical gradient terms

- MathematicsCommunications on Pure and Applied Analysis
- 2023

### On blowup solutions for the mixed fractional Schrödinger equation of Choquard type

- MathematicsNonlinear Analysis
- 2022

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Abstract We develop a systematic study of the superpositions of elliptic operators with different orders, mixing classical and fractional scenarios. For concreteness, we focus on the sum of the…