Abstract
By using the extension of the continuation theorem of Ge and Ren and constructing suitable Banach spaces and operators, we investigate the existence of solutions for a p-Laplacian boundary value problem with integral boundary condition at resonance on the half-line.
Highlights
1 Introduction A boundary value problem is said to be at resonance one if the corresponding homogeneous boundary value problem has non-trivial solutions
Boundary value problems with p-Laplacian have been widely studied owing to their importance in theory and application of mathematics and physics
In [ ], using the continuation theorem of Ge and Ren [ ], the author investigated the existence of solutions for the problem (φp(u )) + f (t, u, u ) =, < t < +∞, u( ) =, φp(u (+∞)) =
Summary
A boundary value problem is said to be at resonance one if the corresponding homogeneous boundary value problem has non-trivial solutions. The p-Laplacian boundary value problems at resonance cannot be solved by Mawhin’s continuation theorem.
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