In 1958, Baker posed the question that if f and g are two permutable transcendental entire functions, must their Julia sets be the same? In order to study this problem of permutable transcendental entire functions, by...In 1958, Baker posed the question that if f and g are two permutable transcendental entire functions, must their Julia sets be the same? In order to study this problem of permutable transcendental entire functions, by the properties of permutable transcendental entire functions, we prove that if f and g are permutable transcendental entire functions, then mes (J(f)) = mes (J(g)). Moreover, we give some results about the zero measure of the Julia sets of the permutable transcendental entire functions family.展开更多
In this paper, the oscillatory behavior for high order nonlinear functional differential equations are studied by means of the Lebesgue measure. It is found that the nonoscillatory solutions only have two kinds on som...In this paper, the oscillatory behavior for high order nonlinear functional differential equations are studied by means of the Lebesgue measure. It is found that the nonoscillatory solutions only have two kinds on some conditions. And necessary conditions for the existence of each kind of nonoscillatory solutions are presented as well. At the same ime, some sufficient conditions for oscillatory solutions are also established.展开更多
In this paper, applying the method of cutting the high order derivative term, we consider the asymptotic characteristic and oscillation of solutions of high order nonlinear neutral functional differential equationswhe...In this paper, applying the method of cutting the high order derivative term, we consider the asymptotic characteristic and oscillation of solutions of high order nonlinear neutral functional differential equationswhere k≥0, m ≥1,n≥2 are all integers.展开更多
文摘In 1958, Baker posed the question that if f and g are two permutable transcendental entire functions, must their Julia sets be the same? In order to study this problem of permutable transcendental entire functions, by the properties of permutable transcendental entire functions, we prove that if f and g are permutable transcendental entire functions, then mes (J(f)) = mes (J(g)). Moreover, we give some results about the zero measure of the Julia sets of the permutable transcendental entire functions family.
文摘In this paper, the oscillatory behavior for high order nonlinear functional differential equations are studied by means of the Lebesgue measure. It is found that the nonoscillatory solutions only have two kinds on some conditions. And necessary conditions for the existence of each kind of nonoscillatory solutions are presented as well. At the same ime, some sufficient conditions for oscillatory solutions are also established.
文摘In this paper, applying the method of cutting the high order derivative term, we consider the asymptotic characteristic and oscillation of solutions of high order nonlinear neutral functional differential equationswhere k≥0, m ≥1,n≥2 are all integers.
