Turkish Journal of Mathematics
DOI
10.3906/mat-1512-64
Abstract
We consider the existence of positive solutions of the nonlinear first order problem with a nonlinear nonlocal boundary condition given by $x^{\prime}(t) = r(t)x(t) + \sum_{i=1}^{m} f_i(t,x(t)), t \in [0,1]$ $\lambda x(0) = x(1) + \sum_{j=1}^{n} \Lambda_j(\tau_j, x(\tau_j)),\tau_j \in [0,1],$ where $r:[0,1] \rightarrow [0,\infty)$ is continuous, the nonlocal points satisfy $0 \leq \tau_1 < \tau_2 < ... < \tau_n \leq 1$, the nonlinear functions $f_i$ and $\Lambda_j$ are continuous mappings from $[0,1] \times [0,\infty) \rightarrow [0,\infty)$ for $i = 1,2,...,m$ and $j = 1,2,...,n$ respectively, and $\lambda >1$ is a positive parameter. The Leray-Schauder theorem and Leggett--Williams fixed point theorem were used to prove our results.
Keywords
Positive solutions, Leray-Schauder fixed point theorem, nonlinear boundary conditions
First Page
350
Last Page
360
Recommended Citation
PATI, SMITA and PADHI, SESHADEV
(2017)
"Positive solutions of first order boundary value problems with nonlinear nonlocal boundary conditions,"
Turkish Journal of Mathematics: Vol. 41:
No.
2, Article 12.
https://doi.org/10.3906/mat-1512-64
Available at:
https://journals.tubitak.gov.tr/math/vol41/iss2/12
