Abstract
The existence of antiperiodic solutions for Liénard-type and Duffing-type differential equations with -Laplacian operator has been studied by using degree theory. The results obtained improve and enrich some known works to some extent.
Highlights
Antiperiodic problems arise naturally from the mathematical models of various of physical processes see 1, 2, and appear in the study of partial differential equations and abstract differential equations see 3–5
For higher-order ordinary differential equations, the existence of antiperiodic solutions was considered in 9–12
Existence results were extended to antiperiodic boundary value problems for impulsive differential equations see, and antiperiodic wavelets were discussed in
Summary
Antiperiodic problems arise naturally from the mathematical models of various of physical processes see 1, 2 , and appear in the study of partial differential equations and abstract differential equations see 3–5. Existence results were extended to antiperiodic boundary value problems for impulsive differential equations see 13 , and antiperiodic wavelets were discussed in 14. The turbulent flow in a porous medium is a fundamental mechanics problem For studying this type of problems, Leibenson see 16 introduced the following p-Laplacian equation: φp x f t, x, x , 1.3 where φp s |s|p−2s, p > 1. A primary purpose of this paper is to study the existence of antiperiodic solutions for the following Lienard-type p-Laplacian equation: φp xfxxgt, x e t. From the arguments in this paper, we can obtain the existence results of periodic solutions for above equations. Our results are different from those of bibliographies listed above
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