Abstract
Abstract This paper explores the existence of solutions for a class of p ( t ) -Laplacian differential systems with multipoint and integral boundary value conditions via Leray-Schauder’s degree. Moreover, the existence of nonnegative solutions is discussed. MSC:34B10.
Highlights
1 Introduction In this paper, we consider the existence of solutions for the following system:
When p(t) is a general function, this paper mainly investigates the existence of solutions for a class of p(t)-Laplacian differential systems with multipoint and integral boundary value conditions
If u is a solution of ( ) with ( ), by integrating ( ) from to t, we find that t φp t, u (t) = φp, u ( ) – g (s) ds
Summary
When p = , the existence of positive solutions for the equation group boundary value problems has been obtained (see [ – ]). When p(t) is a general function, this paper mainly investigates the existence of solutions for a class of p(t)-Laplacian differential systems with multipoint and integral boundary value conditions. We say a function (u, v) : J → RN is a solution of (P) if (u, v) ∈ W satisfies the differential equation in (P) a.e. on J and the boundary value conditions.
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