A CRITERION FOR EXISTENCE OF A POSITIVE SOLUTION OF A NONLINEAR ELLIPTIC SYSTEM

2008 ◽  
Vol 06 (03) ◽  
pp. 299-321 ◽  
Author(s):  
J. VELIN
Keyword(s):  
Positive Solution ◽  
Elliptic System ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Nonlinear Elliptic System ◽  
Nonlinear Elliptic ◽  
Potential Type ◽  
Necessary And Sufficient

In this paper, we give necessary and sufficient conditions for existence of bounded and positive solutions of a nonlinear elliptic system arising from potential type problems.

Decaying positive solutions to a system of nonlinear elliptic equations

2006 ◽  
Vol 136 (2) ◽  
pp. 301-320
Author(s):  
Fenfei Chen ◽  
Miaoxin Yao
Keyword(s):  
Positive Solution ◽  
Elliptic System ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Second Order ◽  
Nonlinear Elliptic System ◽  
Nonlinear Elliptic ◽  
Image Position ◽  
Bounded Below

In this paper, the second-order nonlinear elliptic system with α, γ < 1 and β ≥ 1, is considered in RN, N ≥ 3. Under suitable hypotheses on functions fi, gi, hi (i = 1, 2) and P, it is shown that this system possesses an entire positive solution , 0 < θ < 1, such that both u and v are bounded below and above by constant multiples of |x|2−N for all |x| ≥ 1.

scholarly journals Symmetry and Nonexistence of Positive Solutions for a Fractional Laplacion System with Coupled Terms

2022 ◽  
Author(s):  
Rong Zhang
Keyword(s):  
Positive Solution ◽  
Elliptic System ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Critical Case ◽  
Nonlinear Elliptic System ◽  
Subcritical Case ◽  
Nonlinear Elliptic ◽  
Method Of Moving Planes ◽  
Moving Planes

Abstract In this paper, we study the problem for a nonlinear elliptic system involving fractional Laplacion: (equation 1.1) where 0 < α, β < 2, p, q > 0 and max{p, q} ≥ 1, α + γ > 0, β + τ > 0, n ≥ 2. First of all, while in the subcritical case, i.e. n + α + γ − p(n − α) − (q + 1)(n − β) > 0, n + β + τ − (p + 1)(n − α) − q(n − β) > 0, we prove the nonexistence of positive solution for the above system in R n . Moreover, though Doubling Lemma to obtain the singularity estimates of the positive solution on bounded domain Ω. In addition, while in the critical case, i.e. n+α+γ −p(n−α)−(q + 1)(n−β) = 0, n+β +τ −(p+ 1)(n−α)−q(n−β) = 0, we show that the positive solution of above system are radical symmetric and decreasing about some point by using the method of Moving planes in Rn Mathematics Subject Classification (2020): 35R11, 35A10, 35B06.

scholarly journals Positive solutions of the system of operator equations $A_1X=C_1,XA_2=C_2, A_3XA^*_3=C_3, A_4XA^*_4=C_4$ in Hilbert $C^*$-modules

2018 ◽  
Vol 34 ◽  
pp. 381-388 ◽  
Author(s):  
Rasoul Eskandari ◽  
Xiaochun Fang ◽  
Mohammad Sal Moslehian ◽  
Qingxiang Xu
Keyword(s):  
Positive Solution ◽  
Positive Solutions ◽  
Hilbert Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Operator Equations ◽  
Operator System ◽  
Necessary And Sufficient ◽  
System Of Operator Equations ◽  
Published Result

Necessary and sufficient conditions are given for the operator system $A_1X=C_1$, $XA_2=C_2$, $A_3XA^*_3=C_3$, and $A_4XA^*_4=C_4$ to have a common positive solution, where $A_i$'s and $C_i$'s are adjointable operators on Hilbert $C^*$-modules. This corrects a published result by removing some gaps in its proof. Finally, a technical example is given to show that the proposed investigation in the setting of Hilbert $C^*$-modules is different from that of Hilbert spaces.

scholarly journals Existence of Positive Weak Solutions for a New Class of p,q Laplacian Nonlinear Elliptic System with Sign-Changing Weights

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Rafik Guefaifia ◽  
Salah Mahmoud Boulaaras ◽  
Sultan Alodhaibi ◽  
Salem Alkhalaf
Keyword(s):  
Elliptic System ◽  
Positive Solutions ◽  
Weak Solutions ◽  
Nonlinear Elliptic System ◽  
Bounded Domains ◽  
New Class ◽  
Nonlinear Elliptic ◽  
Sign Conditions

In this paper, by using subsuper solutions method, we study the existence of weak positive solutions for a new class of p,q Laplacian nonlinear elliptic system in bounded domains, when ax, bx,αx, and βx are sign-changing functions that maybe negative near the boundary, without assuming sign conditions on f0,g0,h0, and γ0.

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