This paper deals with the boundary value problem involving the dierential equation
ly := -y''+qy... more This paper deals with the boundary value problem involving the dierential equation ly := -y''+qy = λy, subject to the standard boundary conditions along with the following discontinuity conditions at a point a ε(0,π) y(a + 0) = a1y(a - 0), y'(a + 0) = a1-1y'(a - 0) + a2y(a - 0), where q(x), a1,a2 are real, q ε L2(0,π ) and λ is a parameter independent of x. We develop the Hochestadt's result based on the transformation operator for inverse Sturm-Liouville problem when there are discontinuous conditions. Furthermore, we establish a formula for q(x) - q~(x) in the finite interval where q(x) and q~(x) are analogous functions.
This paper deals with the boundary value problem involving the dierential equation
ly := -y''+qy... more This paper deals with the boundary value problem involving the dierential equation ly := -y''+qy = λy, subject to the standard boundary conditions along with the following discontinuity conditions at a point a ε(0,π) y(a + 0) = a1y(a - 0), y'(a + 0) = a1-1y'(a - 0) + a2y(a - 0), where q(x), a1,a2 are real, q ε L2(0,π ) and λ is a parameter independent of x. We develop the Hochestadt's result based on the transformation operator for inverse Sturm-Liouville problem when there are discontinuous conditions. Furthermore, we establish a formula for q(x) - q~(x) in the finite interval where q(x) and q~(x) are analogous functions.
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ly := -y''+qy = λy,
subject to the standard boundary conditions along with the following
discontinuity conditions at a point a ε(0,π)
y(a + 0) = a1y(a - 0), y'(a + 0) = a1-1y'(a - 0) + a2y(a - 0),
where q(x), a1,a2 are real, q ε L2(0,π ) and λ is a parameter independent of x. We develop the Hochestadt's result based on the transformation operator for inverse Sturm-Liouville problem when there are discontinuous conditions. Furthermore, we establish a formula for q(x) - q~(x) in the finite interval where q(x) and q~(x) are analogous functions.
ly := -y''+qy = λy,
subject to the standard boundary conditions along with the following
discontinuity conditions at a point a ε(0,π)
y(a + 0) = a1y(a - 0), y'(a + 0) = a1-1y'(a - 0) + a2y(a - 0),
where q(x), a1,a2 are real, q ε L2(0,π ) and λ is a parameter independent of x. We develop the Hochestadt's result based on the transformation operator for inverse Sturm-Liouville problem when there are discontinuous conditions. Furthermore, we establish a formula for q(x) - q~(x) in the finite interval where q(x) and q~(x) are analogous functions.