We consider the asymptotic form of the eigenvalues of the linear differential equation \[ -y^{\prime \prime}(x)+q(x) y(x)=\lambda y(x), \quad-\infty<a<x<b<x, \] where \(a<0<b, q(x)\) is singular at \(x=0\), and \(y\) satisfies appropriate conditions at \(a, 0\), and \(b\). This extends previous wo
β¦ LIBER β¦
Dilatation and the asymptotics of the eigenvalues of spectral problems with singularities
β Scribed by V. Ya. Ivrii; S. I. Fedorova
- Publisher
- Springer US
- Year
- 1987
- Tongue
- English
- Weight
- 380 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0016-2663
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## Abstract We consider the nonlinear twoβparameter problem __u__β³(__x__) + __ΞΌu__(__x__)^__p__^ = __Ξ»u__(__x__)^__p__^, __u__(__x__) > 0, __x__ β __I__ = (0, 1), __u__(0) = __u__(1) = 0, where 1 < __q__ < __p__ < 2__q__ + 3 and __Ξ»__, __ΞΌ__ > 0 are parameters. We establish the threeβterm spect