scholarly journals Generalized Emden-Fowler equations of subcritical growth

1993 ◽  
Vol 54 (2) ◽  
pp. 254-262 ◽  
Author(s):  
Wolfgang Rother
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Operator ◽  
Positive Solutions ◽  
Subcritical Growth ◽  
Existence Of Positive Solutions

AbstractThe existence of positive solutions, vanishing at infinity, for the semilinear eigenvalue problem Lu = λ f(x, y) in RN is obtained, where L is a strictly elliptic operator. The function f is assumed to be of subcritical growth with respect to the variable u.

Positive Solutions for the nth-Order Delay Differential System with Multi-Parameter

2011 ◽  
Vol 50-51 ◽  
pp. 185-189
Author(s):  
Qiu Ying Lu ◽  
Wei Peng Zhang
Keyword(s):  
Eigenvalue Problem ◽  
Positive Solutions ◽  
Differential System ◽  
Point Theorem ◽  
Nonlinear Eigenvalue Problem ◽  
Existence Of Positive Solutions ◽  
Delay Differential System ◽  
Delay Differential ◽  
Nonlinear Eigenvalue

In this paper, we are concerned with the existence of positive solutions for the nonlinear eigenvalue problem of the nth-order delay di erential system. The main results in this paper generalize some of the existing results in the literature. Our proofs are based on the well-known Guo-Krasnoselskii xed-point theorem. Three main results are given out, the rst two of which refer to the existence while the last one not only guarantees to its existence but also is pertinent to its multiplicity.

scholarly journals On the existence of positive solutions of Au = λBu

1973 ◽  
Vol 18 (4) ◽  
pp. 281-285
Author(s):  
D. Kershaw
Keyword(s):  
Eigenvalue Problem ◽  
Positive Solutions ◽  
Matrix Equation ◽  
Sufficient Conditions ◽  
Frobenius Theorem ◽  
Positive Vector ◽  
Existence Of Positive Solutions ◽  
The Matrix ◽  
Qualitative Part

It is well known that sufficient conditions for the existence of a positive vector u which satisfies the matrix equation Au = λu are that A should be non-negative and irreducible. This result, the qualitative part of the Perron-Frobenius theorem, has been proved in a variety of ways, one of the most attractive of which is that given by Alexandroff and Hopf in their treatise “ Topologie ”. The aim of this note is to show how their method can be adapted to deal with the generalised eigenvalue problem defined by Au = λBu where A and B are square matrices.

scholarly journals Eigenvalue of Fractional Differential Equations withp-Laplacian Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Wenquan Wu ◽  
Xiangbing Zhou
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Upper And Lower Solutions ◽  
Laplacian Operator ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

We investigate the existence of positive solutions for the fractional order eigenvalue problem withp-Laplacian operator-𝒟tβ(φp(𝒟tαx))(t)=λf(t,x(t)),  t∈(0,1),  x(0)=0,  𝒟tαx(0)=0,  𝒟tγx(1)=∑j=1m-2‍aj𝒟tγx(ξj), where𝒟tβ,  𝒟tα,  𝒟tγare the standard Riemann-Liouville derivatives andp-Laplacian operator is defined asφp(s)=|s|p-2s,  p>1.f:(0,1)×(0,+∞)→[0,+∞)is continuous andfcan be singular att=0,1andx=0.By constructing upper and lower solutions, the existence of positive solutions for the eigenvalue problem of fractional differential equation is established.

scholarly journals AN EIGENVALUE PROBLEM FOR A NON-BOUNDED QUASILINEAR OPERATOR

2004 ◽  
Vol 47 (2) ◽  
pp. 353-363 ◽  
Author(s):  
José Carmona ◽  
Antonio Suárez
Keyword(s):  
Eigenvalue Problem ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Bifurcation Theory ◽  
Bifurcation Parameter ◽  
Quasilinear Elliptic Problem ◽  
Existence Of Positive Solutions ◽  
Positive Eigenfunction ◽  
Quasilinear Elliptic ◽  
Range Of Values

AbstractIn this paper we study the eigenvalues associated with a positive eigenfunction of a quasilinear elliptic problem with an operator that is not necessarily bounded. For that, we use the bifurcation theory and obtain the existence of positive solutions for a range of values of the bifurcation parameter.AMS 2000 Mathematics subject classification: Primary 35J60; 35J25. Secondary 35D05

scholarly journals Positive Solutions for Nonlinearq-Fractional Difference Eigenvalue Problem with Nonlocal Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Wafa Shammakh ◽  
Maryam Al-Yami
Keyword(s):  
Eigenvalue Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
Index Theory ◽  
Nonlocal Boundary Conditions ◽  
Fractional Difference ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

The problem of positive solutions for nonlinearq-fractional difference eigenvalue problem with nonlocal boundary conditions is investigated. Based on the fixed point index theory in cones, sufficient existence of positive solutions conditions is derived for the problem.

scholarly journals Positive Solutions of Eigenvalue Problems for a Class of Fractional Differential Equations with Derivatives

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Xinguang Zhang ◽  
Lishan Liu ◽  
Benchawan Wiwatanapataphee ◽  
Yonghong Wu
Keyword(s):  
Eigenvalue Problem ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Eigenvalue Problems ◽  
Upper And Lower Solutions ◽  
Sufficient Conditions ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
Maximal Principle

By establishing a maximal principle and constructing upper and lower solutions, the existence of positive solutions for the eigenvalue problem of a class of fractional differential equations is discussed. Some sufficient conditions for the existence of positive solutions are established.

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