In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point bo...In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point boundary problems of ordinary differential system of equations.展开更多
Let λ<sub>1</sub>, λ<sub>2</sub>,...,λ<sub>7</sub> be real numbers satisfying λ<sub>i</sub>≥1. In this paper, we prove there are integers x<sub>1</sub>,...Let λ<sub>1</sub>, λ<sub>2</sub>,...,λ<sub>7</sub> be real numbers satisfying λ<sub>i</sub>≥1. In this paper, we prove there are integers x<sub>1</sub>,...,x<sub>7</sub> such that the inequalities |λ<sub>1</sub>x<sub>1</sub><sup>3</sup>+λ<sub>2</sub>x<sub>2</sub><sup>3</sup>+...+λ<sub>7</sub>x<sub>7</sub><sup>3</sup>|【1 and 0【sum from i=1 to7(λ<sub>i</sub>|x<sub>i</sub>]<sup>3</sup> （λ<sub>1</sub>λ<sub>2</sub>…λ<sub>7</sub>）<sup>89814</sup>) hold simultaneously.展开更多
文摘In this paper, we use cone theory and topological degree theory to study superlinear systemof integral equations, and obtain existence theorems for non-trivial solutions; moreover, we applythe results to two-point boundary problems of ordinary differential system of equations.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19671051)
文摘Let λ<sub>1</sub>, λ<sub>2</sub>,...,λ<sub>7</sub> be real numbers satisfying λ<sub>i</sub>≥1. In this paper, we prove there are integers x<sub>1</sub>,...,x<sub>7</sub> such that the inequalities |λ<sub>1</sub>x<sub>1</sub><sup>3</sup>+λ<sub>2</sub>x<sub>2</sub><sup>3</sup>+...+λ<sub>7</sub>x<sub>7</sub><sup>3</sup>|【1 and 0【sum from i=1 to7(λ<sub>i</sub>|x<sub>i</sub>]<sup>3</sup> （λ<sub>1</sub>λ<sub>2</sub>…λ<sub>7</sub>）<sup>89814</sup>) hold simultaneously.
