323 Caudill Jr, L.F. and B.D. Lowe, On the construction of a potential from Cauchy data, Journal of Computational and Applied Mathematics 47 (1993) 323-333. We investigate the problem of recovering a potential q(y) in the differential equation: Llu + q(y)u = 0, (x, y)E(O, l)x(O, 1), u(O, y)=u(l, y)=u(x,0)=0, u(x, l)= f(x), u/x, 1)= g(x). The method of separation of variables reduces the recover...

Abstract The present paper deals with the eigenvalues of complex nonlocal Sturm-Liouville boundary value problems. bounds real and imaginary parts for differential equation involving potential terms associated conditions are obtained in integrable coefficients part eigenvalues.

We consider the spectral function ρ(µ) (µ ≥ 0) for the Sturm-Liouville equation y ′′ + (λ − q)y = 0 on [0, ∞) with the boundary condition y(0) = 0 and where q has slow decay O(x −α) (a > 0) as x → ∞. We develop our previous methods of locating spectral concentration for q with rapid exponential decay (this Journal 81 (1997) 333-348) to deal with the new theoretical and computational complexitie...

Article history: Received 10 December 2010 Available online 18 February 2011 Submitted by Steven G. Krantz

This paper discusses the eigenvalue problem of second-order Sturm-Liouville equation. We transform the governing differential equation to the Fredholm-Volterra integral equation with appropriate end supports. By expanding the unknown function into the shifted Chebyshev polynomials, we directly get the corresponding polynomial characteristic equations, where the lower and higher-order eigenvalue...

The cosmological constant appearing in the Wheeler–De Witt equation is considered as an eigenvalue of the associated Sturm–Liouville problem. A variational approach with Gaussian trial wave functionals is used as a method to study such a problem. We approximate the equation to one loop in a Schwarzschild background and a zeta function regularization is involved to handle with divergences. The r...