Remark on kneser problem

On Kneser Solutions of Nonlinear Third Order Differential Equations

“…(4) on T ∞). Then, according to [1], there exists a solution x of (1) such that x t > 0, x t < 0 for t large. In order to complete the proof, it is sufficient to apply Theorems 1 and 6 in [3].…”

“…y + q t y + r t f y = 0 (1) where q r ∈ C 0 R + R + = 0 ∞ f ∈ C 0 R . Throughout the paper r > 0 on R + f x > 0 for x > 0 f 0 = 0 H1 will be supposed.…”

“…The existence and the asymptotic behaviour of Kneser solutions have been investigated by many authors (see, e.g., [1], the monographies [9,13], and the references therein) if either q ≤ 0 or in the linear case f x ≡ x.…”

On the behavior of Kneser solutions of nonlinear ordinary differential equations

“…In the literature, solutions of problem (1.1), (1.2) are also known as Kneser solutions. Starting from the pioneering paper of A. Kneser [7], they attract the attention of many mathematicians [1][2][3][4][5][6][7][8][9][10]. Our aim is to obtain priory estimates and sufficient conditions for any solution of (1.1), (1.2) to be singular of the first kind.…”