Existence and nonexistence of solutions to cone elliptic equations via Galerkin method

2021 ◽  
Author(s):  
Thi Thu Huong Nguyen ◽  
Nhu Thang Nguyen
Keyword(s):  
Galerkin Method ◽  
Elliptic Equations ◽  
Existence And Nonexistence ◽  
Nonexistence Of Solutions

QUASILINEAR ELLIPTIC EQUATIONS WITH SINGULAR QUADRATIC GROWTH TERMS

2011 ◽  
Vol 13 (04) ◽  
pp. 607-642 ◽  
Author(s):  
LUCIO BOCCARDO ◽  
TOMMASO LEONORI ◽  
LUIGI ORSINA ◽  
FRANCESCO PETITTA
Keyword(s):  
Positive Solutions ◽  
Lebesgue Space ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Quadratic Growth ◽  
Open Set ◽  
Existence And Nonexistence ◽  
Nonexistence Of Solutions ◽  
Quasilinear Problems ◽  
Quasilinear Elliptic

In this paper, we deal with positive solutions for singular quasilinear problems whose model is [Formula: see text] where Ω is a bounded open set of ℝN, g ≥ 0 is a function in some Lebesgue space, and γ > 0. We prove both existence and nonexistence of solutions depending on the value of γ and on the size of g.

scholarly journals The Solvability of Fractional Elliptic Equation with the Hardy Potential

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Siyu Gao ◽  
Shuibo Huang ◽  
Qiaoyu Tian ◽  
Zhan-Ping Ma
Keyword(s):  
Elliptic Equation ◽  
Lipschitz Domain ◽  
Sobolev Inequality ◽  
Elliptic Equations ◽  
Sharp Constant ◽  
Hardy Potential ◽  
Bounded Lipschitz Domain ◽  
Existence And Nonexistence ◽  
Nonexistence Of Solutions ◽  
Fractional Laplace Operator

In this paper, we study the existence and nonexistence of solutions to fractional elliptic equations with the Hardy potential −Δsu−λu/x2s=ur−1+δgu,in Ω,ux>0,in Ω,ux=0,in ℝN∖Ω, where Ω⊂ℝN is a bounded Lipschitz domain with 0∈Ω, −Δs is a fractional Laplace operator, s∈0,1, N>2s, δ is a positive number, 2<r<rλ,s≡N+2s−2αλ/N−2s−2αλ+1, αλ∈0,N−2s/2 is a parameter depending on λ, 0<λ<ΛN,s, and ΛN,s=22sΓ2N+2s/4/Γ2N−2s/4 is the sharp constant of the Hardy–Sobolev inequality.

scholarly journals Global existence and nonexistence for a class of finitely degenerate coupled parabolic systems with high initial energy level

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yuxuan Chen ◽  
Jiangbo Han
Keyword(s):  
Energy Level ◽  
Global Existence ◽  
Blow Up ◽  
Parabolic Systems ◽  
Initial Energy ◽  
Blowup Time ◽  
Positive Initial Energy ◽  
Existence And Nonexistence ◽  
Nonexistence Of Solutions ◽  
Coupled Parabolic Systems

<p style='text-indent:20px;'>In this paper, we consider a class of finitely degenerate coupled parabolic systems. At high initial energy level <inline-formula><tex-math id="M1">\begin{document}$ J(u_{0})&gt;d $\end{document}</tex-math></inline-formula>, we present a new sufficient condition to describe the global existence and nonexistence of solutions for problem (1)-(4) respectively. Moreover, by applying the Levine's concavity method, we give some affirmative answers to finite time blow up of solutions at arbitrary positive initial energy <inline-formula><tex-math id="M2">\begin{document}$ J(u_{0})&gt;0 $\end{document}</tex-math></inline-formula>, including the estimate of upper bound of blowup time.</p>

Sign in / Sign up

Export Citation Format

Share Document