Abstract
Abstract In this paper, we study the existence of solutions of a class of higher-order integro-differential boundary value problems with ϕ-Laplacian like operator and functional boundary conditions. By giving the definition of a pair of coupled lower and upper solutions and some new hypotheses, we obtain some new existence results for boundary value problems with ϕ-Laplacian like operator by employing the Schauder fixed point theorem and an appropriate Nagumo condition. Finally, an example is given to illustrate the results. MSC:39K10, 34B15.
Highlights
Integro-differential equations have become more and more important in some mathematical models of real phenomena, especially in control, biological, medical, and informational models
Boundary value problems (BVPs) for nonlinear integro-differential equations are used to describe a great number of nonlinear phenomena in science, the theory of φ-Laplacian BVPs has emerged as an important area in recent years
We found that BVP ( . ) and ( . ) is more general in the literature, and the functional boundary condition ( . ) may cover many classical boundary conditions, such as various linear two-point, multi-point studied by many authors, but it may include many new boundary conditions not studied so far in the literature
Summary
Integro-differential equations have become more and more important in some mathematical models of real phenomena, especially in control, biological, medical, and informational models. We will consider the following BVPs of higher-order functional integro-differential φ-Laplacian like equations with functional boundary conditions: φ u(n– )(t) + Au(t) = , t ∈ J , gi(u, W u, S u, . ), that is, a function u(t) ∈ Cn– [ , T] such that φ(u(n– )) is absolutely continuous on J , u(t) satisfies A variety of methods and tools, such as lower and upper solution methods and various fixed point theorems, are very useful and have been successfully used to prove the existence of solutions of BVPs. Motivated by the above mentioned works, we consider the BVPs of higher-order functional integro-differential equations
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