Let a∈N.In this paper we prove that if Jacobi symbol, then the rsophantine equation y2=ax4 + x3 + 2(a - 1)x= + x + (a - 2) has no integer soutions, except a = ( is a square), x = 2,and a -2 = , x = 0, Whre 2(mod6), Q...Let a∈N.In this paper we prove that if Jacobi symbol, then the rsophantine equation y2=ax4 + x3 + 2(a - 1)x= + x + (a - 2) has no integer soutions, except a = ( is a square), x = 2,and a -2 = , x = 0, Whre 2(mod6), Qk denote Fibonacci-Lucas se-guence defined by Qn+2 = Qn+1 + Qn, Q0 = 2,Q1 =1.展开更多
In this paper, we establish the existence of upper and lower solutions for a periodic boundary value problems (PBVP for short) of impulsive differential equations. which guarantees the existence of at least one soluti...In this paper, we establish the existence of upper and lower solutions for a periodic boundary value problems (PBVP for short) of impulsive differential equations. which guarantees the existence of at least one solution for the problem. As an application, these results are applied to PBVP of ODE and some examples are given to illustrate our results.展开更多
文摘Let a∈N.In this paper we prove that if Jacobi symbol, then the rsophantine equation y2=ax4 + x3 + 2(a - 1)x= + x + (a - 2) has no integer soutions, except a = ( is a square), x = 2,and a -2 = , x = 0, Whre 2(mod6), Qk denote Fibonacci-Lucas se-guence defined by Qn+2 = Qn+1 + Qn, Q0 = 2,Q1 =1.
文摘In this paper, we establish the existence of upper and lower solutions for a periodic boundary value problems (PBVP for short) of impulsive differential equations. which guarantees the existence of at least one solution for the problem. As an application, these results are applied to PBVP of ODE and some examples are given to illustrate our results.
