scholarly journals Positive solutions to a nonlinear eigenvalue problem

2020 ◽  
Vol 21 (01) ◽  
pp. 18-22
Author(s):  
Yong-Hui Zhou
Keyword(s):  
Eigenvalue Problem ◽  
Positive Solutions ◽  
Nonlinear Eigenvalue Problem ◽  
Nonlinear Eigenvalue

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.

Positive solutions of a non-linear eigenvalue problem with discontinuous non-linearity

1979 ◽  
Vol 83 (1-2) ◽  
pp. 133-145 ◽  
Author(s):  
Paolo Nistri
Keyword(s):  
Eigenvalue Problem ◽  
Positive Solutions ◽  
Nonlinear Eigenvalue Problem ◽  
Linear Term ◽  
Linear Eigenvalue Problem ◽  
Existence And Multiplicity ◽  
Non Linear ◽  
Nonlinear Eigenvalue

SynopsisWe seek non-trivial solutions (u,λ)∈C1([0,1])×[0,∞ with u(x)≧0 for all x ∈[0,1], of the nonlinear eigenvalue problem –u″(x)=λf(u(x)) for x ∈ (0,1) and u(0)=u(1)=0,where f:[0,∞)→[0,∞) is such that f(p) = 0, for p ∈ [0,1), and f(p) = K(p), for p ∈ (1,∞), and K: [1, ∞)→(0, ∞) is assumed to be twice continuously differentiable. (The value ƒ(1) is only required to be positive.)Existence and multiplicity theorems are given in the cases where ƒ is asymptotically sub-linear and ƒ is asymptotically super-linear. Moreover if strengthened assumptions are made on the growth of the non-linear term ƒ we obtain the precise number of non-trivial solutions for given values of λ ∈ [0, ∞).

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