A class of second-order nonlocal indefinite impulsive differential systems

作者：Jiao, Lishuai; Zhang, Xuemei^*

来源：Boundary Value Problems, 2018, 2018(1): 163.

DOI：10.1186/s13661-018-1082-z

• Indefinite weights
• Nonlocal impulsive differential system
• Positive solutions
• Existence and multiplicity
• Fixed point technology

We consider the second-order nonlocal impulsive differential system
{-x '' = a(t)xy + omega(t)f(x), 0 < t < 1, t not equal t(k,)
-y '' = b(t)x, 0 < t < 1, t not equal t(k,)
Delta x vertical bar(t=tk) = J(k)(x(t(k))), k = 1,2,...,n,
Delta y vertical bar(t=tk) = J(k)(y(t(k))), k = 1,2,...,n,
x(0) = integral(1)(0) h(t)x(t)dt, x'(1) = 0,
y(0) = integral(1)(0) g(t)y(t)dt, y'(1) = 0,
where the weight functions a(t), b(t), and omega(t) change sign on [0,1], and g( t) not equivalent to 0 and h(t) not equivalent to 0 on [0,1]. By constructing a cone K-1 x K-2, which is the Cartesian product of two cones in space PC[0,1], and applying the well-known fixed point theorem of cone expansion and compression in K-1 x K-2, we obtain conditions for the existence and multiplicity of positive solutions of a nonlocal indefinite impulsive differential system. An example is given to illustrate the main results.

• 出版日期2018-10-25
• 单位华北电力大学（保定）; 华北电力大学