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- W4386251089 abstract "In this paper, we consider the modified Kirchhoff type equation, that is, the Kirchhoff type equation with a quasilinear term (1) {−(a+b∫R3|∇u|2dx)Δu+V(|x|)u−12Δ(|u|2)u=|u|p−2uin R3,u→0as |x|→∞,(1) where a, b>0, p∈(4,22∗) and V(|x|) is a radial potential function and bounded below by a positive number. The appearance of nonlocal term b∫R3|∇u|2dxΔu and quasilinear term 12Δ(|u|2)u makes the variational functional of (1) totally different from the classical Schrödinger equation. By introducing the Miranda theorem, via a construction and gluing method, for any given integer k≥ 1, we prove that Equation (1) admits a radial nodal solution Ukb having exactly k nodes. Moreover, the energy of Ukb is monotonically increasing in k and for any sequence {bn}, and up to a subsequence, Ukbn converges strongly to some Uk0≠ 0 as bn→0+, which is a nodal solution with exactly k nodes to the local quasilinear Schrödinger equation (2) {−aΔu+V(|x|)u−12Δ(|u|2)u=|u|p−2uin R3,u→0as |x|→∞.(2) These results improve and generalize the previous results in the literature from the local quasilinear Schrödinger equation to the nonlocal quasilinear Kirchhoff equation." @default.
- W4386251089 created "2023-08-30" @default.
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- W4386251089 date "2023-08-29" @default.
- W4386251089 modified "2023-09-27" @default.
- W4386251089 title "Infinitely many nodal solutions for a modified Kirchhoff type equation" @default.
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- W4386251089 doi "https://doi.org/10.1080/17476933.2023.2246901" @default.
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