scholarly journals A-priori bounds and existence for solutions of weighted elliptic equations with a convection term

2017 ◽  
Vol 6 (4) ◽  
pp. 427-445 ◽  
Author(s):  
Ky Ho ◽  
Inbo Sim
Keyword(s):  
Elliptic Equations ◽  
Neumann Boundary Condition ◽  
Existence Of Solutions ◽  
A Priori ◽  
Neumann Boundary ◽  
Variable Exponents ◽  
Convection Term ◽  
Pseudomonotone Operators ◽  
A Priori Bounds ◽  
Localization Method

AbstractWe investigate weighted elliptic equations containing a convection term with variable exponents that are subject to Dirichlet or Neumann boundary condition. By employing the De Giorgi iteration and a localization method, we give a-priori bounds for solutions to these problems. The existence of solutions is also established using Brezis’ theorem for pseudomonotone operators.

A priori estimates for superlinear and subcritical elliptic equations: the Neumann boundary condition case

2011 ◽  
Vol 137 (3-4) ◽  
pp. 525-544 ◽  
Author(s):  
Abdellaziz Harrabi ◽  
Mohameden Ould Ahmedou ◽  
Salem Rebhi ◽  
Abdelbaki Selmi
Keyword(s):  
Boundary Condition ◽  
Elliptic Equations ◽  
Neumann Boundary Condition ◽  
A Priori Estimates ◽  
A Priori ◽  
Neumann Boundary ◽  
Priori Estimates

scholarly journals Loop Type Subcontinua of Positive Solutions for Indefinite Concave-Convex Problems

2019 ◽  
Vol 19 (2) ◽  
pp. 391-412
Author(s):  
Uriel Kaufmann ◽  
Humberto Ramos Quoirin ◽  
Kenichiro Umezu
Keyword(s):  
Elliptic Equations ◽  
Bifurcation Theory ◽  
A Priori ◽  
Global Bifurcation ◽  
Neumann Boundary ◽  
Zero Solution ◽  
Regularization Scheme ◽  
Convex Problems ◽  
Nonnegative Solutions ◽  
Indefinite Weights

AbstractWe establish the existence of loop type subcontinua of nonnegative solutions for a class of concave-convex type elliptic equations with indefinite weights, under Dirichlet and Neumann boundary conditions. Our approach depends on local and global bifurcation analysis from the zero solution in a nonregular setting, since the nonlinearities considered are not differentiable at zero, so that the standard bifurcation theory does not apply. To overcome this difficulty, we combine a regularization scheme with a priori bounds, and Whyburn’s topological method. Furthermore, via a continuity argument we prove a positivity property for subcontinua of nonnegative solutions. These results are based on a positivity theorem for the associated concave problem proved by us, and extend previous results established in the powerlike case.

scholarly journals Existence of Solutions to Elliptic Problem with Convection Term and Lower-Order Term

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xiaohua He ◽  
Shuibo Huang ◽  
Qiaoyu Tian ◽  
Yonglin Xu
Keyword(s):  
Dirichlet Problem ◽  
Lower Order ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Order Term ◽  
Combined Effects ◽  
Convection Term ◽  
Bounded Smooth Domain ◽  
Bounded Smooth ◽  
Lower Order Terms

In this paper, we establish the existence of solutions to the following noncoercivity Dirichlet problem − div M x ∇ u + u p − 1 u = − div u E x + f x , x ∈ Ω , u x = 0 , x ∈ ∂ Ω , where Ω ⊂ ℝ N N > 2 is a bounded smooth domain with 0 ∈ Ω , f belongs to the Lebesgue space L m Ω with m ≥ 1 , p > 0 . The main innovation point of this paper is the combined effects of the convection terms and lower-order terms in elliptic equations.

scholarly journals ON AN ELLIPTIC SYSTEM OF P(X)-KIRCHHOFF-TYPE UNDER NEUMANN BOUNDARY CONDITION

2012 ◽  
Vol 17 (2) ◽  
pp. 161-170 ◽  
Author(s):  
Zehra Yucedag ◽  
Mustafa Avci ◽  
Rabil Mashiyev
Keyword(s):  
Boundary Condition ◽  
Weak Solution ◽  
Variational Principle ◽  
Variational Method ◽  
Elliptic System ◽  
Neumann Boundary Condition ◽  
Existence Of Solutions ◽  
Neumann Boundary ◽  
Kirchhoff Type ◽  
Direct Variational Method

In the present paper, by using the direct variational method and the Ekeland variational principle, we study the existence of solutions for an elliptic system of p(x)-Kirchhoff-type under Neumann boundary condition and show the existence of a weak solution.

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