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Positive solutions of a second-order nonlinear Robin problem involving the first-order derivative
- Source :
- Advances in Difference Equations, Vol 2021, Iss 1, Pp 1-16 (2021)
- Publication Year :
- 2021
- Publisher :
- SpringerOpen, 2021.
-
Abstract
- Abstract This paper is concerned with the second-order nonlinear Robin problem involving the first-order derivative: { u ″ + f ( t , u , u ′ ) = 0 , u ( 0 ) = u ′ ( 1 ) − α u ( 1 ) = 0 , $$ \textstyle\begin{cases} u''+f(t,u,u^{\prime })=0, \\ u(0)=u'(1)-\alpha u(1)=0,\end{cases} $$ where f ∈ C ( [ 0 , 1 ] × R + 2 , R + ) $f\in C([0,1]\times \mathbb{R}^{2}_{+},\mathbb{R}_{+})$ and α ∈ ] 0 , 1 [ $\alpha \in ]0,1[$ . Based on a priori estimates, we use fixed point index theory to establish some results on existence, multiplicity and uniqueness of positive solutions thereof, with the unique positive solution being the limit of of an iterative sequence. The results presented here generalize and extend the corresponding ones for nonlinearities independent of the first-order derivative.
Details
- Language :
- English
- ISSN :
- 16871847
- Volume :
- 2021
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Advances in Difference Equations
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.13e760e0032d4dbaa1f0e425fe877d97
- Document Type :
- article
- Full Text :
- https://doi.org/10.1186/s13662-021-03465-y