Existence theory for positive solutions to one-dimensional p-Laplacian boundary value problems on time scales
By Hong‐Rui Sun, Wan-Tong Li. 2007
91 citations recorded by the source corpus.
Abstract In this paper we consider the one-dimensional p-Laplacian boundary value problem on time scales ( φ p ( u Δ ( t ) ) ) Δ + h ( t ) f ( u σ ( t ) ) = 0 , t ∈ [ a , b ] , u ( a ) − B 0 ( u Δ ( a ) ) = 0 , u Δ ( σ ( b ) ) = 0 , where φ p ( u ) is p-Laplacian operator, i.e., φ p ( u ) = | u | p − 2 u , p > 1 . Some new results are obtained for the existence of at least single, twin or triple positive solutions of the above problem by using Krasnosel'skii's fixed point theorem, new fixed point theorem due to Avery and Henderson and Leggett–Williams fixed point theorem. This is probably the first time the existence of positive solutions of one-dimensional p-Laplacian boundary value problems on time scales has been studied.
Subfields: Applied Mathematics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/c41e0d2c6f7efcb9b5ac4880cc5f1dab530db28c
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In Applied Mathematics
- Carlos Lizama
- Jaqueline Godoy Mesquita
- Gaston M. N'Guérékata
- Christopher S. Goodrich
- Chuang Chen
- Miao Li
- Rodrigo Ponce
- V. Keyantuo
In Control and Systems Engineering
Citations in the corpus
- Almost automorphic solutions of dynamic equations on time scales (2013, background): “Because of this fact, it has been attracting the attention of many mathematicians (see [1], [6], [10], [22], [23], [24], [26], [27], [45], [46], [47], [48], for instance and the references therein) and the interest in the subject remains growing.”