On eigenfunctions of the boundary value problems for second order differential equations with involution
Sarsenbi A. Sarsenbi A.
October 2021MDPI
Symmetry
2021#13Issue 10
We give a definition of Green’s function of the general boundary value problems for non-self-adjoint second order differential equation with involution. The sufficient conditions for the basis property of system of eigenfunctions are established in the terms of the boundary conditions. Uniform equiconvergence of spectral expansions related to the second-order differential equations with involution:−y′′ (x) + αy′′ (−x) + q(x)y(x) = λy(x), −1 < x < 1, with the boundary conditions y′ (−1) + b1 y(−1) = 0, y′ (1) + b2 y(1) = 0, is obtained. As a corollary, it is proved that the eigenfunctions of the perturbed boundary value problems form the basis in L2 (−1, 1) for any complex-valued coefficient q(x) ∈ L1 (−1, 1).
Basis , Boundary value problem , Differential equation , Eigenfunction , Eigenvalue , Green’s function , Involution
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Department of Mathematics, M. Auezov South Kazakhstan University, Shymkent, 160000, Kazakhstan
Department of Mathematics
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