We start this work by recalling a class of globally hypoelliptic sublaplacians defined on the N-dimensional torus introduced by Cordaro and Himonas in 1994 and studied by Himonas and Petronilho in 2000. We consider a new ...

In this work, we consider first a class of concave-convex type elliptical problems with sing-changing weight functions that satisfy some additional conditions. Still, we work with the magnetic laplacian operator. We prove ...

In this work, we study existence and multiplicity of weak solutions for three problems involving fractional operators, with emphasis on critical growth nonlinearities. The first problem deals with the existence of sign-changing ...

This work is dedicated to the study of dynamical properties of some partial differential equations (PDE, for short) of parabolic type, local or nonlocal ones. We prove existence, uniqueness and establish the asymptotic ...

This thesis is concerned with the orbital instability for a specific class of periodic traveling wave solutions with the mean zero related to the modified Camassa-Holm equation. These solutions, called snoidal waves, are ...

In this thesis, we study equations that involving the Dirac operator and which have the form $-i \alpha \cdot \nabla u + a \beta u + M(x)u = F_{u}(x,u), em \mathbb{R}^{3},$ where $\alpha = (\alpha_1, \alpha_2, \alpha_3),$ ...

Mathematical Analysis; Littlewood-Paley's decomposition; Bony's decomposition; Navier-Stokes's system

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