In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions i...In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions in the literature.展开更多
This paper gives the rules of oscillations of two classes of neutraldifferential equations with forced terms, and some oscillation criteria undercertain conditions are presented according to the equations having diffe...This paper gives the rules of oscillations of two classes of neutraldifferential equations with forced terms, and some oscillation criteria undercertain conditions are presented according to the equations having differentcharacters.展开更多
This paper is concerned with the existence of eventually positive solutions and oscillatory solutions of first-order neutral differential equation with positive and negative coefficients. The 'sharp' condition...This paper is concerned with the existence of eventually positive solutions and oscillatory solutions of first-order neutral differential equation with positive and negative coefficients. The 'sharp' conditions of oscillation for the equation have been obtained, i.e., the conditions are sufficient and necessary when all of the coefficients are constants. These conditions are distinguished from the previous criteria in the literatures, and also weaker than those existing results.展开更多
Some comparison theorems of the non-existence of positive solutions are derived for a classof neutral type difference equations with positive and negative coefficients. These results extendand improve some comparison ...Some comparison theorems of the non-existence of positive solutions are derived for a classof neutral type difference equations with positive and negative coefficients. These results extendand improve some comparison criteria obtained in the literature [1] and [2].展开更多
In this paper,some new properties of solutions of the first order nonlinear differential inequalities with deviating arguments are given.These results improve many corresponding ones in the literature.
Positive entire solutions of the equation where 1 〈 p ≤ N, q 〉 0, are classified via their Morse indices. It is seen that there is a critical power q = qc such that this equation has no positive radial entire solut...Positive entire solutions of the equation where 1 〈 p ≤ N, q 〉 0, are classified via their Morse indices. It is seen that there is a critical power q = qc such that this equation has no positive radial entire solution that has finite Morse index when q 〉 qc but it admits a family of stable positive radial entire solutions when 0 〈 q ≤ qc- Proof of the stability of positive radial entire solutions of the equation when 1 〈 p 〈 2 and 0 〈 q ≤ qc relies on Caffarelli-Kohn Nirenberg＇s inequality. Similar Liouville type result still holds for general positive entire solutions when 2 〈 p ≤ N and q 〉 qc. The case of 1 〈 p 〈 2 is still open. Our main results imply that the structure of positive entire solutions of the equation is similar to that of the equation with p = 2 obtained previously. Some new ideas are introduced to overcome the technical difficulties arising from the p-Laplace operator.展开更多
基金the National Natural Science Foundation of China(1 0 0 71 0 1 8)
文摘In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions in the literature.
文摘This paper gives the rules of oscillations of two classes of neutraldifferential equations with forced terms, and some oscillation criteria undercertain conditions are presented according to the equations having differentcharacters.
基金Research supported by National Natural Science Foundation of P. R. China (10071016) by Foundation of the Education Department for Excellent Teacher of University.
文摘This paper is concerned with the existence of eventually positive solutions and oscillatory solutions of first-order neutral differential equation with positive and negative coefficients. The 'sharp' conditions of oscillation for the equation have been obtained, i.e., the conditions are sufficient and necessary when all of the coefficients are constants. These conditions are distinguished from the previous criteria in the literatures, and also weaker than those existing results.
文摘Some comparison theorems of the non-existence of positive solutions are derived for a classof neutral type difference equations with positive and negative coefficients. These results extendand improve some comparison criteria obtained in the literature [1] and [2].
文摘In this paper,some new properties of solutions of the first order nonlinear differential inequalities with deviating arguments are given.These results improve many corresponding ones in the literature.
基金supported by NSFC(Grant Nos.11171092 and 11571093)supported by NSFC(Grant No.11371117)
文摘Positive entire solutions of the equation where 1 〈 p ≤ N, q 〉 0, are classified via their Morse indices. It is seen that there is a critical power q = qc such that this equation has no positive radial entire solution that has finite Morse index when q 〉 qc but it admits a family of stable positive radial entire solutions when 0 〈 q ≤ qc- Proof of the stability of positive radial entire solutions of the equation when 1 〈 p 〈 2 and 0 〈 q ≤ qc relies on Caffarelli-Kohn Nirenberg＇s inequality. Similar Liouville type result still holds for general positive entire solutions when 2 〈 p ≤ N and q 〉 qc. The case of 1 〈 p 〈 2 is still open. Our main results imply that the structure of positive entire solutions of the equation is similar to that of the equation with p = 2 obtained previously. Some new ideas are introduced to overcome the technical difficulties arising from the p-Laplace operator.
