Аннотация:
In this paper, we consider an iterative system of nonlinear nth order differential equations:
y(n)i(t)+λipi(t)fi(yi+1(t))=0,1≤i≤m,ym+1(t)=y1(t),t∈[0,1],
with three-point non-homogeneous boundary conditions
yi(0)=yi′(0)=⋯=y(n−2)i(0)=0,αiy(n−2)i(1)−βiy(n−2)i(η)=μi,1≤i≤m,
where n≥3,η∈(0,1), μi∈(0,∞) is a parameter, fi:R+→R+ is continuous,
pi:[0,1]→R+ is continuous and pi does not vanish identically on any closed subinterval of [0,1] for 1≤i≤m.
We express the solution of the boundary value problem as a solution of an equivalent integral equation involving kernels and
obtain bounds for these kernels. By an application of Guo–Krasnosel'skii fixed point theorem on a cone in a Banach space, we determine intervals
of the eigenvalues λ1,λ2,⋯,λm for which the boundary value problem possesses a positive solution.
As applications, we provide examples demonstrating our results.
Образец цитирования:
K. R. Prasad, M. Rashmita, N. Sreedhar, “Solvability of higher order three-point iterative systems”, Уфимск. матем. журн., 12:3 (2020), 109–124; Ufa Math. J., 12:3 (2020), 107–122
К. Р. Прасад, Б. Сравани, Н. Сридхар, “Счетное множество положительных решений итеративной системы краевых задач на временных шкалах”, Изв. вузов. Матем., 2024, № 10, 61–76
Kanakayya Namana, Sreedhar Namburi, Rajendra Prasad Kapula, “Positivity results to iterative system of higher order boundary value problems”, J. Appl. Math., 2:5 (2024), 1829
К. Р. Прасад, Н. Шридхар, М. Рашмита, “Разрешимость итерационной системы дифференциальных уравнений дробного порядка с неоднородными граничными условиями”, Изв. вузов. Матем., 2023, № 6, 74–88
K. R. Prasad, N. Sreedhar, M. Rashmita, “Solvability of Iterative System of Fractional Order Differential Equations with Nonhomogeneous Boundary Conditions”, Russ Math., 67:6 (2023), 63
Bouzid Mansouri, Abdelouaheb Ardjouni, Ahcene Djoudi, “Positive solutions of nonlinear fourth order iterative differential equations with two-point and integral boundary conditions”, Nonautonomous Dynamical Systems, 8:1 (2021), 297