Abstract
In this paper, we study the second-order impulsive boundary value problem ? Lu = f ( x , u ) , x ? [ 0 , 1 ] ? { x 1 , x 2 , ? , x l } , ? Δ ( p ( x i ) u ? ( x i ) ) = I i ( u ( x i ) ) , i = 1 , 2 , ? , l , R 1 ( u ) = 0 , R 2 ( u ) = 0 , $$\left\{\begin{array}{ll} -Lu=f(x, u), \, \, x\in [0, 1]\backslash\{x_{1}, x_{2}, \cdots, x_{l}\}, \\ -{\Delta} (p(x_{i}) u'(x_{i}))=I_{i}(u(x_{i})), \quad i=1, 2, \cdots, l, \\ R_{1}(u)=0, \, \, \, R_{2}(u)=0, \end{array}\right.$$ where Lu = (p(x)u?)? ? q(x)u is a Sturm-Liouville operator, R 1(u) = ?u?(0) ? βu(0) and R 2(u) = ?u?(1) + ?u(1). The existence of sign-changing and multiple solutions is obtained. The technical approach is based on minimax methods and invariant sets of descending flow.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
