EXISTENCE OF THREE SOLUTIONS FOR HEMIVARIATIONAL INEQUALITIES DRIVEN WITH IMPULSIVE EFFECTS

Document Type : Original Article

Authors
Neamat Nyamoradi 1
Kaimin Teng 2
1 Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran.
2 Department of Mathematics, Taiyuan University of Technology, 030024 Taiyuan, Shanxi, People’s Republic of China.
10.29252/maco.1.1.4
Abstract
In this paper we prove the existence of at least three solutions to the following
second-order impulsive system:
−(ρ(x) ˙u)
′ + A(x)u ∈ λ(∂j(x, u(x)) + µ∂k(x, u(x))), a.e. t ∈ (0, T),
∆(ρ(x) ˙u
i
(xj )) = ρ(x
+
j
) ˙u
i
(x
+
j
) − ρ(x
−
j
) ˙u
i
(x
−
j
) = Iij (u
i
(xj )),
i = 1, . . . , N, j = 1, . . . , l,
α1u˙(0) − α2u(0) = 0, β1u˙(T) + β2u(T) = 0,
where A : [0, T] → R
N×N is a continuous map from the interval [0, T] to the set of N-order symmetric matrixes. The approach is fully based on a recent three critical points theorem of Teng [K. Teng, Two nontrivial solutions for hemivariational inequalities driven by nonlocal elliptic operators, Nonlinear Anal. (RWA) 14 (2013) 867-874].

Keywords

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Mathematical Analysis and Convex Optimization
Volume 1, Issue 1
June 2020
Pages 25-39