### Existence of positive solutions to impulsive nonlinear differential systems of second order with two point boundary conditions

#### Abstract

point boundary value problem for nonlinear second-order impulsive systems.

They use a vector version of Krasnosel'skii's fixed point theorem in cones in their proofs. Examples are provided to illustrate the results.

#### Keywords

#### Full Text:

PDF#### References

H. Abdeli, J. R. Graef, H. Kadari, A. Ouahab, and A. Oumansour, Existence of solutions to systems of second-order impulsive differential equation with integral boundary condition on the half-line, {em Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal.} {bf 29} (2022), 91--209.

O. Bolojan-Nica, G. Infante, and P. Pietramala, Existence results for impulsive systems with initial nonlocal conditions, {em Math. Model. Anal.} {bf 18} (2013), 599--611.

H. Berrezoug, J. Henderson, and A. Ouahab, Existence and uniqueness of solutions for a system of impulsive differential equations on the half-line, {em J. Nonlinear. Funct. Anal.} {bf 2017} (2017), Article ID 38, 1--16.

S. Djebali, T. Moussaoui, and R. Precup, Fourth-Order p-Laplacian nonlinear systems via the vector version of Krasnosel'skii's fixed point theorem, {em Mediterr. J. Math.} {bf 6} (2009), 447--460.

J. R. Graef, J. Henderson, and A. Ouahab, {em Topological Methods for Differential Equations and Inclusions}, Monographs and Research Notes in Mathematics, CRC Press, Boca Raton, 2019.

J. R. Graef, H. Kadari, A. Ouahab, and A. Oumansour, Existence results for systems of second-order impulsive differential equations, {em Acta Math. Univ. Comenian. (N.S.)} {bf 88} (2019), 51--66.

D. Herlea, Existence and localization of positive solutions to first order differential systems with nonlocal conditions, {em Babes-Bolyai Math.} {bf 59} (2014), 221--231.

Y. He, Existence of positive solutions to second-order periodic boundary value problems with impulse actions, {em Theoretical Math. Appl.} {bf 4} (2014), 79--91.

X. Lin and D. Jiang, Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations, {em J. Math. Anal. Appl.} {bf 321} (2006), 501--514.

L. Liu, L. Hu, and Y. Wu, Positive solutions of nonlinear singular two-point boundary value problems for second-order impulsive differential equations, {em App. Math. Comput.} {bf 196} (2008), 550--562.

L. Liu, L. Hu, and Y. Wu, Positive solutions of two-point boundary value problems for systems of nonlinear second-order singular and impulsive differential equations, {em Nonlinear Anal.} {bf 69} (2008), 3774--3789.

X. Liu and Y. Li, Positive solutions for Neumann boundary value problems of second-order impulsive differential equations in Banach spaces, {em Abstract Appl. Anal.} {bf 2012} (2012), Article ID 401923, 1--14.

R. Precup, A vector version of Krasnosel'skii's fixed point theorem in cones and positive periodic solutions of nonlinear systems, {em J. Fixed Point Theory Appl.} {bf 2} (2007), 141--151.

R. Precup, Positive solutions of nonlinear systems via the vector version of Krasnosel'skii's fixed point theorem in cones, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity 5 (2007), 129--138.

DOI: http://dx.doi.org/10.24193/subbmath.2024.3.10

### Refbacks

- There are currently no refbacks.