On the zeros of meromorphic solutions of second-order linear differential equations

Oscillation results on y″ + Ay = 0 in the complex domain with transcendental entire coefficients which have extremal deficiencies

“…It is shown in [2] that E(z) satisfies both where the path of integration is taken within the domain s/.…”

“…Let E: = e z " where n^2 is a positive integer. Then Bank and Laine [1] (see also [2]) show that £ is a product of two linearly independent solutions of 1 _ 2z n 2 2n-2 n-2 4 where A(z)= -\e~2 zn and P(z)= -i(n 2 z 2n~2 + 2n(2n-l)z n~2 ).…”

“…Now although the coefficients C t and C o in (6.12) of the equation (6.11) have bounds depending on the polynomial P(z), in any case it is true that they both are bounded by a constant multiple of r" + 2 for r (and hence j) sufficiently large and for n ^ 0. So we let r,( r ) 2 …”

Second Order Differential Equations with Rational Coefficients

“…Indeed fx(z) = ez(z-l)/z and f2(z) = e~z(z+ l)/z have only real zeros and poles and solve (1.1) with 77(z) = -1 -2z . So as in Theorem A, we assume fxf2 to be transcendental which implies that at least one of /, and f2 has infinitely many zeros [1,Theorem 1]. Then by Theorem A, we have di(77) = 0.…”

Value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations

“…Many scholars applied Nevanlinna theory and its difference analogues to study the properties of meromorphic solutions of complex differential equations and complex difference equations, and obtained fruitful achievement (see [4][5][6][7][8]). Especially, it is an essential respect to study the oscillation property of meromorphic solutions of complex differential equations and complex difference equations.…”