On the critical $p$-Kirchhoff equation
نویسندگان
چکیده
We study a nonlocal elliptic equation of $p$-Kirchhoff type involving the critical Sobolev exponent. First we give sufficient conditions for $(\text{PS})$ condition to hold. Then prove some existence and multiplicity results using tools from Morse theory, in particular, notion cohomological local splitting eigenvalues based on Fadell-Rabinowitz index.
منابع مشابه
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: Topological Methods in Nonlinear Analysis
سال: 2023
ISSN: ['1230-3429']
DOI: https://doi.org/10.12775/tmna.2021.061