Positive solutions of boundary value problems with nonlinear nonlocal boundary conditions

• Autorzy: Padhi S. , Pati S. , Hota D. K.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2016.36.l.69

• Języki publikacji: EN

Abstrakty

EN

We consider the existence of at least three positive solutions of a nonlinear first order problem with a nonlinear nonlocal boundary condition given by [formula] where r : [0,1] → [0, ∞) is continuous; the nonlocal points satisfy [formula] the nonlinear function ƒi and [formula] are continuous mappings from [0,1] x [0,∞) → [0,∞) for i = 1,2,... ,m and j = 1, 2,. .. , n respectively, and λ > 0 is a positive parameter.

Słowa kluczowe

EN

positive solutions; Leggett-Williams fixed point theorem; nonlinear boundary conditions

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2016
• Tom: Vol. 36, no. 1
• Strony: 69--79
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Padhi S.

• Birla Institute ol Technology Department ol Mathematics Mesra, Ranchi - 835215, India

autor

Pati S.

• Birla Institute ol Technology Department ol Mathematics Mesra, Ranchi - 835215, India

autor

Hota D. K.

• Indira Gandhi Institute ol Technology Department ol Mechanical System Design Sarang - 759146, India

Bibliografia

• [1] D.R. Anderson, Existence of three solutions for a first-order problem with nonlinear nonlocal boundary conditions, J. Math. Anal. Appl. 408 (2013), 318-323.
• [2] D. Bai, Y. Xu, Periodic solutions of first order functional differential equations with periodic deviations, Comp. Math. Appl. 53 (2007), 1361-1366.
• [3] J.G. Dix, S. Padhi, Existence of multiple positive periodic solutions for delay differential equation whose order is a multiple of 4, Appl. Math. Comput. 216 (2010), 2709-2717.
• [4] J.R. Graef, S. Padhi, S. Pati, Periodic solutions of some models with strong Allee effects, Nonlinear Anal. Real World Appl. 13 (2012), 569-581.
• [5] J.R. Graef, S. Padhi, S. Pati, Existence and nonexistence of multiple positive periodic solutions of first order differential equations with unbounded Green's kernel, Panamer. Math. J. 23 (2013) 1, 45-55.
• [6] J.R. Graef, S. Padhi, S. Pati, Multiple positive periodic solutions of first order ordinary differential equations with unbounded Green's Kernel, Commun. Appl. Anal. 17 (2013), 319-330.
• [7] J.R. Graef, S. Padhi, S. Pati, P.K. Kar, Positive solutions of differential equations with unbounded Green's Kernel, Appl. Anal. Discrete Math. 6 (2012), 159-173.
• [8] R.W. Leggett, L.R. Williams, Multiple positive fixed points of nonlinear operators on ordered Banach Spaces, Indiana Univ. Math. J. 28 (1979), 673-688.
• [9] S. Padhi, C. Qian, S. Srivastava, Multiple periodic solutions for a first order nonlinear functional differential equation with applications to population dynamics, Commun. Appl. Anal. 12 (2008) 3, 341-352.
• [10] S. Padhi, S. Srivastava, Existence of three periodic solutions for a nonlinear first order functional differential equation, J. Franklin Inst. 346 (2009), 818-829.
• [11] S. Padhi, S. Srivastava, J.G. Dix, Existence of three nonnegative periodic solutions for functional differential equations and applications to hematopoiesis, Panamer. Math. J. 19 (2009) 1, 27-36.
• [12] S. Padhi, P.D.N. Srinivasu, G.K. Kumar, Periodic solutions for an equation governing dynamics of a renewable resource subjected to Allee effects, Nonlinear Anal. Real World Appl. 11 (2010), 2610-2618.
• [13] S. Padhi, S. Srivastava, S. Pati, Three periodic solutions for a nonlinear first order functional differential equation, Appl. Math. Comput. 216 (2010), 2450-2456.
• [14] S. Padhi, S. Srivastava, S. Pati, Positive periodic solutions for first order functional differential equations, Commun. Appl. Anal. 14 (2010), 447-462.
• [15] S. Pati, J.R. Grael, S. Padhi, P.K. Kar, Periodic solutions of a single species renewable resources under periodic habitat fluctuations with harvesting and Allee effect, Comm. Appl. Nonl. Anal. 20 (2013), 1-16.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.