Oscillatory properties of fourth order self-adjoint differential equations
Fišnarová, Simona
Archivum Mathematicum, Tome 040 (2004), p. 457-469 / Harvested from Czech Digital Mathematics Library
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Oscillation and nonoscillation criteria for the self-adjoint linear differential equation \[ (t^\alpha y^{\prime \prime })^{\prime \prime }-\frac{\gamma _{2,\alpha }}{t^{4-\alpha }}y=q(t)y,\quad \alpha \notin \lbrace 1, 3\rbrace \,, \] where \[ \gamma _{2,\alpha }=\frac{(\alpha -1)^2(\alpha -3)^2}{16}\] and $q$ is a real and continuous function, are established. It is proved, using these criteria, that the equation \[\left(t^\alpha y^{\prime \prime }\right)^{\prime \prime }-\left(\frac{\gamma _{2,\alpha }}{t^{4-\alpha }} + \frac{\gamma }{t^{4-\alpha }\ln ^2 t}\right)y = 0\] is nonoscillatory if and only if $\gamma \le \frac{\alpha ^2-4\alpha +5}{8}$.

Publié le : 2004-01-01
Classification:  34C10 
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     author = {Simona Fi\v snarov\'a},
     title = {Oscillatory properties of fourth order self-adjoint differential equations},
     journal = {Archivum Mathematicum},
     volume = {040},
     year = {2004},
     pages = {457-469},
     zbl = {1117.34038},
     mrnumber = {2129965},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107927}
}

Fišnarová, Simona. Oscillatory properties of fourth order self-adjoint differential equations. Archivum Mathematicum, Tome 040 (2004) pp. 457-469. http://gdmltest.u-ga.fr/item/107927/

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