EXISTENCE AND APPROXIMATION OF SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SECOND ORDER ITERATIVE DIFFERENTIAL EQUATIONS

Dedicated to the memory of Professor Mihail Megan

 

Vasile Berinde†

Abstract: We study the existence and approximation of solutions to the second-order iterative boundary-value problem x”(t) = f(t, x(t), x[2](t)), 0≤t≤1, where x[2](t) ; = x(x(t)), with solutions satisfying one of the two sets of boundary conditions: (i)   x(0) = 0, x(1) = 1;     (ii) x(0) = 1, x(1) = 0.

Keywords: ordinary differential equation, boundary value problem, fixed point, contraction mapping, nonexpansive mapping.

MSC: 47H10, 47H05, 54H25, 34K05, 34A12.

DOI  10.56082/annalsarscimath.2026.3.185

Read full articleEXISTENCE AND APPROXIMATION OF SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SECOND ORDER ITERATIVE DIFFERENTIAL EQUATIONS                                                                                Download articleEXISTENCE AND APPROXIMATION OF SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SECOND ORDER ITERATIVE DIFFERENTIAL EQUATIONS

*Accepted for publication on July 30, 2026
†vasile.berinde@mi.utcluj.ro, Department of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Victoriei 76, 430122 Baia Mare, Romania; Academy of Romanian Scientists

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 3, 2026

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997