Existence of solutions for elliptic equations with discontinuous nonlinearities strong resonance at infinity

2009 ◽  
Vol 70 (12) ◽  
pp. 4441-4450 ◽  
Author(s):  
Xian Wu
Keyword(s):  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Strong Resonance ◽  
Discontinuous Nonlinearities

scholarly journals Existence of Solutions for Unbounded Elliptic Equations with Critical Natural Growth

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Aziz Bouhlal ◽  
Abderrahmane El Hachimi ◽  
Jaouad Igbida ◽  
El Mostafa Sadek ◽  
Hamad Talibi Alaoui
Keyword(s):  
Elliptic Problem ◽  
Lebesgue Space ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Regularity Of Solutions ◽  
Natural Growth ◽  
Existence And Regularity Results ◽  
Regularity Results

We investigate existence and regularity of solutions to unbounded elliptic problem whose simplest model is {-div[(1+uq)∇u]+u=γ∇u2/1+u1-q+f  in  Ω,  u=0  on  ∂Ω,}, where 0<q<1, γ>0 and f belongs to some appropriate Lebesgue space. We give assumptions on f with respect to q and γ to show the existence and regularity results for the solutions of previous equation.

scholarly journals Super and subsolutions for elliptic equations on all ofℝn

2002 ◽  
Vol 32 (1) ◽  
pp. 41-46
Author(s):  
G. A. Afrouzi ◽  
H. Ghasemzadeh
Keyword(s):  
Population Genetics ◽  
Elliptic Equation ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Asymptotic Properties ◽  
Semilinear Elliptic Equation ◽  
Semilinear Elliptic

By construction sub and supersolutions for the following semilinear elliptic equation−△u(x)=λg(x)f(u(x)),x∈ℝnwhich arises in population genetics, we derive some results about the theory of existence of solutions as well as asymptotic properties of the solutions for everynand for the functiong:ℝn→ℝsuch thatgis smooth and is negative at infinity.

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.

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