Abstract
By constructing a suitable projection scheme and using the extension of Mawhin’s continuation theorem, the existence of solution for functional p-Laplacian boundary value problems at resonance is studied. The paper is a generalization of some current results to a fully nonlinear case.
Highlights
1 Introduction A boundary value problem is said to be at resonance if the corresponding homogeneous boundary value problem has a non-trivial solution
In Refs. [6, 9], the authors studied the existence of solutions for functional boundary value problems with a linear differential operator by using Mawhin’s continuation theorem
Since the p-Laplacian operator occurs in many applications such as non-Newtonian mechanics, nonlinear elasticity and glaciology, combustion theory, we would like to further extend the results of [6] to the third-order functional p-Laplacian boundary value problem at resonance
Summary
A boundary value problem is said to be at resonance if the corresponding homogeneous boundary value problem has a non-trivial solution. [6, 9], the authors studied the existence of solutions for functional boundary value problems with a linear differential operator by using Mawhin’s continuation theorem.
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