Abstract
In this paper, we study the existence of coupled solutions of anti-periodic boundary value problems for impulsive differential equations with ϕ-Laplacian operator. Based on a pair of coupled lower and upper solutions and appropriate Nagumo condition, we prove the existence of coupled solutions for anti-periodic impulsive differential equations boundary value problems with ϕ-Laplacian operator.
Highlights
The study boundary value problems (BVPs for short) with p -Laplacian operator has been emerging as an important area and obtained a considerable attention
-Laplacian operator appears in the study of flow through porous media ( p = 3 / 2 ), nonlinear elasticity ( p ≥ 2 ), glaciology ( 1 ≤ p ≤ 4 / 3 ) and so on, there are many works about existence of solutions for differential equations with p
This section is devoted to proving the existence of coupled solutions for anti-periodic impulsive differential equations boundary value problems with φ -Laplacian operator
Summary
The study boundary value problems (BVPs for short) with p -Laplacian operator has been emerging as an important area and obtained a considerable attention. -Laplacian operator appears in the study of flow through porous media ( p = 3 / 2 ), nonlinear elasticity ( p ≥ 2 ), glaciology ( 1 ≤ p ≤ 4 / 3 ) and so on, there are many works about existence of solutions for differential equations with p. Guo and Gu [22] study a class of nonlinear impulsive differential equation with anti-periodic boundary condition:. In [22], the authors obtained the existence of solution for anti-periodic boundary value problems (1)-(3).
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