scholarly journals Singular quasilinear convective elliptic systems in ℝ N

2022 ◽  
Vol 11 (1) ◽  
pp. 741-756
Author(s):  
Umberto Guarnotta ◽  
Salvatore Angelo Marano ◽  
Abdelkrim Moussaoui
Keyword(s):  
Fixed Point ◽  
Weak Solution ◽  
Elliptic System ◽  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Systems ◽  
Perturbation Techniques ◽  
Priori Estimates ◽  
Regularity Results

Abstract The existence of a positive entire weak solution to a singular quasi-linear elliptic system with convection terms is established, chiefly through perturbation techniques, fixed point arguments, and a priori estimates. Some regularity results are then employed to show that the obtained solution is actually strong.

scholarly journals Quasilinear elliptic systems in divergence form associated to general nonlinearities

2018 ◽  
Vol 7 (4) ◽  
pp. 425-447 ◽  
Author(s):  
Lorenzo D’Ambrosio ◽  
Enzo Mitidieri
Keyword(s):  
Positive Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Systems ◽  
Divergence Form ◽  
Systems Of Equations ◽  
Quasilinear Elliptic Systems ◽  
Open Set ◽  
Priori Estimates ◽  
Quasilinear Elliptic

AbstractThe paper is concerned with a priori estimates of positive solutions of quasilinear elliptic systems of equations or inequalities in an open set of {\Omega\subset\mathbb{R}^{N}} associated to general continuous nonlinearities satisfying a local assumption near zero. As a consequence, in the case {\Omega=\mathbb{R}^{N}}, we obtain nonexistence theorems of positive solutions. No hypotheses on the solutions at infinity are assumed.

scholarly journals Positive solutions of a diffusive two competitive species model with saturation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Aung Zaw Myint
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Existence Of Solution ◽  
Priori Estimates ◽  
Competitive Species ◽  
Coexistence State ◽  
Fixed Point Indices ◽  
Stability Results

<p style='text-indent:20px;'>In this paper, the positive solutions of a diffusive two competitive species model with Bazykin functional response are investigated. We give the a priori estimates and compute the fixed point indices of trivial and semi-trivial solutions. And obtain the existence of solution and demonstrate the bifurcation of a coexistence state emanating from semi-trivial solutions. Finally, multiplicity and stability results are presented.</p>

Mathematical modeling of wave propagation in viscoelastic media with the fractional Zener model

2021 ◽  
Vol 8 (4) ◽  
pp. 601-615
Author(s):  
M. Ait Ichou ◽  
◽  
H. El Amri ◽  
A. Ezziani ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Wave Propagation ◽  
Weak Solution ◽  
A Priori Estimates ◽  
A Priori ◽  
Zener Model ◽  
Priori Estimates ◽  
Dissipative Media ◽  
Fractional Zener Model ◽  
Model Existence

The question of interest for the presented study is the mathematical modeling of wave propagation in dissipative media. The generalized fractional Zener model in the case of dimension d (d=1,2,3) is considered. This work is devoted to the mathematical analysis of such model: existence and uniqueness of the strong and weak solution and energy decay result which guarantees the wave dissipation. The existence of the weak solution is shown using a priori estimates for solutions which are also presented.

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