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Properties of the least action level and the existence of ground state solution to fractional elliptic equation with harmonic potential

100%

Ledesma C. E. T. , Gutierrez H. C. , Rodríguez J. A. , Bonilla M. M.

Opuscula Mathematica

2024

tom Vol. 44, no. 5

749--765

In this article we consider the following fractional semilinear elliptic equation [formula]. By using variational methods we show the existence of a symmetric decreasing ground state solution of this equation. Moreover, we study some continuity and differentiability properties of the ground state level. Finally, we consider a bifurcation type result.

Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian

58%

Bidi Y. , Beniani A. , Zennir K. , Himadan A.

Demonstratio Mathematica

2021

tom Vol. 54, nr 1

245--258

We consider strong damped wave equation involving the fractional Laplacian with nonlinear source. The results of global solution under necessary conditions on the critical exponent are established. The existence is proved by using the Galerkin approximations combined with the potential well theory. Moreover, we showed new decay estimates of global solution.