Necessary and Sufficient Conditions of Existence for Positive Solution to a Class of Quasilinear Elliptic Systems in R N

2009 ◽  
Vol 110 (2) ◽  
pp. 771-783
Author(s):  
Guoqing Zhang ◽  
Sanyang Liu
Keyword(s):  
Positive Solution ◽  
Sufficient Conditions ◽  
Elliptic Systems ◽  
Necessary And Sufficient Conditions ◽  
Quasilinear Elliptic Systems ◽  
Necessary And Sufficient ◽  
Quasilinear Elliptic

scholarly journals Existence and uniqueness of positive eigenfunctions for certain eigenvalue systems

2004 ◽  
Vol 173 ◽  
pp. 65-84
Author(s):  
Ru-Ying Xue ◽  
Yi-Min Yang
Keyword(s):  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Elliptic Systems ◽  
Necessary And Sufficient Conditions ◽  
Quasilinear Elliptic Systems ◽  
Necessary And Sufficient ◽  
Quasilinear Elliptic

AbstractThe existence and uniqueness of eigenvalues and positive eigenfunctions for some quasilinear elliptic systems are considered. Some necessary and sufficient conditions which guarantee the existence and uniqueness of eigenvalues and positive eigenfunctions are given.

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.

scholarly journals Solutions to the System of Operator EquationsA1X=C1,XB2=C2, andA3XB3=C3on HilbertC*-Modules

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaochun Fang ◽  
Enran Hou ◽  
Ge Dong
Keyword(s):  
General Solution ◽  
Positive Solution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Operator Equations ◽  
Existence Of A Solution ◽  
Necessary And Sufficient

We study the solvability of the system of the adjointable operator equationsA1X=C1,XB2=C2, andA3XB3=C3over HilbertC*-modules. We give necessary and sufficient conditions for the existence of a solution and a positive solution of the system. We also derive representations for a general solution and a positive solution to this system. The above results generalize some recent results concerning the equations for operators with closed ranges.

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.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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