The following equation is considered in this paper:
class="formula" id="fm0010">
where
α,
β and
γ are real parameters and
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16303249&_mathId=si2.gif&_user=111111111&_pii=S0022247X16303249&_rdoc=1&_issn=0022247X&md5=cbdd4368b842b49e933864e14415ac9e" title="Click to view the MathML source">γ>0class="mathContainer hidden">class="mathCode">. This equation is referred to as Mathieu's equation when
class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16303249&_mathId=si3.gif&_user=111111111&_pii=S0022247X16303249&_rdoc=1&_issn=0022247X&md5=b89fe6caa5ef12ab0463c55b890d7cc3" title="Click to view the MathML source">γ=2class="mathContainer hidden">class="mathCode">. The parameters determine whe
ther all solutions of this equation are oscillatory or nonoscillatory. Our results provide parametric conditions for oscillation and nonoscillation;
there is a feature in which it is very easy to check whe
ther
these conditions are satisfied or not. Parametric oscillation and nonoscillation regions are drawn to help understand
the obtained results.