Samuel Azubuike IYASE, Ogbu Famous IMAGA

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

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.

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[1] Agarwal RP, O’ Regan D. Infinite interval problems for differential, difference and integral equations. Kluwer Academic, 2001.
[2] Agarawal RP, O’ Regan D. (Eds) Series in Mathematical analysis and applications. Vol. 3. Gordon and Breach Science Publishers (2001).
[3] Frioui A, Guezane-Lakoud A, Khaldi A. Higher order boundary value problems at resonance on an unbounded interval. Electronic Journal of Differential Equations 2016; 4:1-10.
[4] Gupta CP. A non-resonant multipoint boundary value problem of Neumann-Dirichlet type for a p-Laplacian type operator. Dynamical Systems and Applications 2004; 4: 439-442.
[5] Hopkins B, Kosmatov N. Third-order boundary value problems with sign-changing solutions. Nonlinear Analysis TMA 2007; 67: 126-137.
[6] Iyase SA. On a third-order boundary value problem at resonance on the half-lin. Araian Journal of Mathematics 2019; 8: 43-53. doi: 202007 540065 – 018-0209-5
[7] Kim CG. Solvability of multipoint boundary value problems on the half-line. Journal of Nonlinear Science and Applications 2012; 5: 27-33.
[8] Kosmatov N. Second order boundary value problems on an unbounded domain. Nonlinear Analysis TMA 2008; 688: 2158-2171.
[9] Lian H, Ge W. Solvability of second order three point boundary value problems on the half-line. Applied Mathematical Letters 2003; 16: 33-39.
[10] O’Regan D, Precup R. Theorems of Leray-Schauder type and applications. CRC Press, 2002.
[11] Zeidler E. Nonlinear functional analysis and its applications. Springer-Verlag, New York, 1986.