Abstract
This paper concerned with the existence of solutions of anti-periodic boundary value problems for impulsive differential equations with φ-Laplacian operator. Firstly, the definition a pair of coupled lower and upper solutions of the problem is introduced. Then, under the approach of coupled upper and lower solutions together with Nagumo condition, we prove that there exists at least one solution of anti-periodic boundary value problems for impulsive differential equations with φ-Laplacian operator.
Highlights
We will study a class of nonlinear impulsive differential equation with φ-Laplacian operator and anti-periodic boundary conditions as following: (φ(u′(t)))′ = f (t,u(t),u′(t)) a.e. t ∈[0,T ], P, (1)
We will deduce that there exists at least one solution of the problem (1)-(3) lying between a pair of coupled lower and upper solutions
We mainly discuss the existence of solutions of anti-periodic boundary value problems for impulsive differential equations with φ-Laplacian operator
Summary
We will study a class of nonlinear impulsive differential equation with φ-Laplacian operator and anti-periodic boundary conditions as following:. Cabada and Tomecek [4] focussed on the φ-Laplacian differential equations (1) subject to impulsive functions (2) with non-local boundary conditions g2. As far as we known, the papers [4, 6, 8] study such a general φ-Laplacian problems with nonlinear boundary conditions, but its didn’t contain the anti-periodic problems. There are few dependent references for studying the φ-Laplacian impulsive functional differential equations with anti-periodic boundary condition. Anti-periodic boundary conditions appear in difference and differential equations (see [16, 17] and references therein).
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