A third-order p-laplacian boundary value problem on an unbounded domain

Abstract

In this work, we apply Leray-Schauder continuation principle to establish the existence of at least one solution to the third order p-Laplacian boundary value problem on an unbounded domain of the form (w(t)φp(u ′′ (t))) ′ = K(t, u(t), u ′ (t), u ′′ (t)), t ∈ (0,∞) u(0) = 0, u ′ (0) = Σm i=1 αi ∫ ξi 0 u(t)dt, lim t→∞ (w(t)φp(u ′′ (t)) = 0 under the nonresonant condition Σm i=1 αiξ2 ̸= 2.