Article
MSC:
34B20,
35C10,
47B25,
47E05,
73K12,
74H45,
74K20 | MR 0961312 | Zbl 0658.73037 | DOI: 10.21136/AM.1988.104315
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Keywords:
positive definite; compact resolvent; Fourier method; existence theorems; static; transverse static deflection; transverse vibration; thin homogeneous elastic plate; transverse load; dynamic problems; circular plates theory
positive definite; compact resolvent; Fourier method; existence theorems; static; transverse static deflection; transverse vibration; thin homogeneous elastic plate; transverse load; dynamic problems; circular plates theory
Summary:
The operator $L_0:D_{L_0}\subset H \rightarrow H$, $L_0u = \frac 1r \frac d {dr} \left\{r \frac d{dr}\left[\frac 1r \frac d{dr}\left(r \frac {du}{dr}\right)\right] \right\}$, $D_{L_0}= \{u \in C^4 ([0,R]), u'(0)=u''''(0)=0, u(R)=u'(R)=0\}$, $H=L_{2,r}(0,R)$ is shown to be essentially self-adjoint, positive definite with a compact resolvent. The conditions on $L_0$ (in fact, on a general symmetric operator) are given so as to justify the application of the Fourier method for solving the problems of the types $L_0u=g$ and $u_{tt}+L_0u=g$, respectively.
References:
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