Existence of positive solutions of advanced differential equations

In this paper, we study the advanced differential equations [ r ( t ) | x ′ ( t ) | α − 1 x ′ ( t ) ] ′ + ∑ i = 1 n p i ( t ) | x ( t + τ i ( t ) ) | α − 1 x ( t + τ i ( t ) ) = 0 and [ r ( t ) ( y ( t ) − P ( t ) y ( t − τ ) ) ′ ] ′ + ∑ i = 1 n p i ( t ) f ( y ( t + σ ) ) = 0 . By using the general...

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Bibliographic Details
Published in:Advances in difference equations 2013-06, Vol.2013 (1), p.158-158, Article 158
Main Authors: Li, Qiaoluan, Liu, Xiaojing, Cui, Feifei, Li, Weina
Format: Article
Language:English
Subjects:
Analysis
Difference and Functional Equations
Functional Analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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Summary:In this paper, we study the advanced differential equations [ r ( t ) | x ′ ( t ) | α − 1 x ′ ( t ) ] ′ + ∑ i = 1 n p i ( t ) | x ( t + τ i ( t ) ) | α − 1 x ( t + τ i ( t ) ) = 0 and [ r ( t ) ( y ( t ) − P ( t ) y ( t − τ ) ) ′ ] ′ + ∑ i = 1 n p i ( t ) f ( y ( t + σ ) ) = 0 . By using the generalized Riccati transformation and the Schauder-Tyichonoff theorem, we establish the conditions for the existence of positive solutions of the above equations. MSC: 34K11, 39A10.
ISSN:1687-1847
1687-1847
DOI:10.1186/1687-1847-2013-158