Superlinear Kirchhoff-type problems of the fractional p-Laplacian without the (AR) condition

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The Kirchhoff Equation for the P – Laplacian

wt t (t, x)− K (‖wx (t, ·)‖ β Lr (R))a(wx (t, x))wxx (t, x) = 0, (2) w(0, x) = 8(x), wt (0, x) = 9(x), where K is an arbitrary function, sufficiently smooth and taking only positive values; and a = a(s) behaves like |s|p−2 near s = 0. The detailed assumptions on K , r , β, and a are given in (3), (4) and Condition 1 below. For K = K (s) = c1 + c2s (c1, c2 > 0) and p = r = β = 2, we get the famo...

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ژورنال

عنوان ژورنال: Boundary Value Problems

سال: 2018

ISSN: 1687-2770

DOI: 10.1186/s13661-018-1100-1