Abstract
In this paper, we investigate the best fit solution for the second order differential problem with one initial and other integral conditions. We obtain the representation of that minimizer and present an example.paration.
Highlights
In the paper [2], there was studied the best fit solution to the second order differential problem with one initial condition and other nonlocal two point condition.Let us continue the investigation taking the integral condition−u′′ = f (x), x ∈ [0, 1], (1)ξ u(0) = g1, u(1) = γ u(x) dx + g2, (2)where f ∈ L2[0, 1], g1, g2, γ ∈ R and ξ ∈ (0, 1)
We investigate the best fit solution for the second order differential problem with one initial and other integral conditions
We obtain the representation of that minimizer and present an example
Summary
In the paper [2], there was studied the best fit solution to the second order differential problem with one initial condition and other nonlocal two point condition. If the parameter γ = 0, this problem becomes classical, it is uniquely solvable and has the Green’s function. For nonvanishing values of the parameter γ, the problem (1)–(2) becomes nonlocal. If γξ2 = 2 [3], it has the unique solution, which is of the form u. For γξ2 = 2, the problem (1)–(2) does not have the unique solution. This is the case that we are going to study below and obtain the so called best fit solution
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