Abstract
Abstract In this work we investigate the completeness, minimality and basis properties of the eigenfunctions of one class discontinuous Sturm-Liouville equation with a spectral parameter in boundary conditions.
Highlights
We consider the boundary value problem for the differential equation on the interval [−1, 1](u) :≡ −u + q(x)u = λ w(x)u, (1)with the boundary conditionsL1(u) := u(−1) + hu (−1) = 0, (2)L2(u) := (β1u(1) − β2u (1)) + λ β1u(1) − β2u (1) = 0, (3)and the transmission conditionsL3(y) := γ1u(−0) − δ1u(+0) = 0, (4)
In this work we investigate the completeness, minimality and basis properties of the eigenfunctions of one class discontinuous Sturm-Liouville equation with a spectral parameter in boundary conditions
The goal of this work is to investigate the problem of completeness, minimality and basis property of the eigenfunctions of the boundary value problem (1)-(5)
Summary
Abstract In this work we investigate the completeness, minimality and basis properties of the eigenfunctions of one class discontinuous Sturm-Liouville equation with a spectral parameter in boundary conditions. On eigenvalues problems for second order equation with spectral parameter in the boundary conditions are considered in [5,6,7,8,9,10,11,12,13, 20,21,22]. Some self adjoint problems on eigenvalues for second order equation with spectral parameter in the boundary conditions are considered in [5,6,7,8,9,10,11].
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