Abstract
This paper investigates the existence and asymptotic behavior of solutions for weighted -Laplacian system multipoint boundary value problems in half line. When the nonlinearity term satisfies sub-( ) growth condition or general growth condition, we give the existence of solutions via Leray-Schauder degree.
Highlights
Where p ∈ C 0, ∞, R, p t > 1, limt → ∞p t exists and limt → ∞p t > 1, −Δp t u − w t |u |p t −2u is called the weighted p t -Laplacian; w ∈ C 0, ∞, R satisfies 0 < w t, for all t ∈ 0, ∞, and w t −1/ p t −1 ∈ L1 0, ∞ ; the equivalent limr → 0 w r |u |p r −2u r limr → ∞w r |u |p r −2u r means that limr → 0 w r |u |p r −2u r and limr → ∞w r |u |p r −2u r both exist and equal; δ is a positive parameter
In this paper, when p t is a general function, we investigate the existence and asymptotic behavior of solutions for weighted p t -Laplacian systems with multi-point boundary value conditions
If u is a solution of 2.4 with 1.2, by integrating 2.4 from 0 to t, we find that t w t φ t, u t w 0 φ 0, u 0 g s ds
Summary
This paper investigates the existence and asymptotic behavior of solutions for weighted p t Laplacian system multipoint boundary value problems in half line.
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