Existence of nontrivial weak solutions for p-biharmonic Kirchhoff-type equations

Jung Hyun Bae; Jae Myoung Kim; Jongrak Lee; Kisoeb Park

doi:10.1186/s13661-019-1237-6

Existence of nontrivial weak solutions for p-biharmonic Kirchhoff-type equations

Jung Hyun Bae
, Jae Myoung Kim
, Jongrak Lee
, Kisoeb Park

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We are concerned with the following p-biharmonic equations: Δp2u+M(∫RNΦ0(x,∇u)dx)div(φ(x,∇u))+V(x)|u|p−2u=λf(x,u)in RN, where 2 < 2 p< N, Δp2u=Δ(|Δu|p−2Δu), the function φ(x, v) is of type | v| ^p ⁻ ²v, φ(x,v)=ddvΦ0(x,v), the potential function V: R^N→ (0 , ∞ ) is continuous, and f: R^N× R→ R satisfies the Carathéodory condition. We study the existence of weak solutions for the problem above via mountain pass and fountain theorems.

Original language	English
Article number	125
Journal	Boundary Value Problems
Volume	2019
Issue number	1
DOIs	https://doi.org/10.1186/s13661-019-1237-6
State	Published - 1 Dec 2019
Externally published	Yes

Keywords

Kirchhoff type
p-biharmonic
Variational method

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10.1186/s13661-019-1237-6

Cite this

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title = "Existence of nontrivial weak solutions for p-biharmonic Kirchhoff-type equations",

abstract = "We are concerned with the following p-biharmonic equations: Δp2u+M(∫RNΦ0(x,∇u)dx)div(φ(x,∇u))+V(x)|u|p−2u=λf(x,u)in RN, where 2 < 2 p< N, Δp2u=Δ(|Δu|p−2Δu), the function φ(x, v) is of type | v| p − 2v, φ(x,v)=ddvΦ0(x,v), the potential function V: RN→ (0 , ∞ ) is continuous, and f: RN× R→ R satisfies the Carath{\'e}odory condition. We study the existence of weak solutions for the problem above via mountain pass and fountain theorems.",

keywords = "Kirchhoff type, p-biharmonic, Variational method",

author = "Bae, \{Jung Hyun\} and Kim, \{Jae Myoung\} and Jongrak Lee and Kisoeb Park",

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year = "2019",

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doi = "10.1186/s13661-019-1237-6",

language = "English",

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T1 - Existence of nontrivial weak solutions for p-biharmonic Kirchhoff-type equations

AU - Bae, Jung Hyun

AU - Kim, Jae Myoung

AU - Lee, Jongrak

AU - Park, Kisoeb

PY - 2019/12/1

Y1 - 2019/12/1

N2 - We are concerned with the following p-biharmonic equations: Δp2u+M(∫RNΦ0(x,∇u)dx)div(φ(x,∇u))+V(x)|u|p−2u=λf(x,u)in RN, where 2 < 2 p< N, Δp2u=Δ(|Δu|p−2Δu), the function φ(x, v) is of type | v| p − 2v, φ(x,v)=ddvΦ0(x,v), the potential function V: RN→ (0 , ∞ ) is continuous, and f: RN× R→ R satisfies the Carathéodory condition. We study the existence of weak solutions for the problem above via mountain pass and fountain theorems.

AB - We are concerned with the following p-biharmonic equations: Δp2u+M(∫RNΦ0(x,∇u)dx)div(φ(x,∇u))+V(x)|u|p−2u=λf(x,u)in RN, where 2 < 2 p< N, Δp2u=Δ(|Δu|p−2Δu), the function φ(x, v) is of type | v| p − 2v, φ(x,v)=ddvΦ0(x,v), the potential function V: RN→ (0 , ∞ ) is continuous, and f: RN× R→ R satisfies the Carathéodory condition. We study the existence of weak solutions for the problem above via mountain pass and fountain theorems.

KW - Kirchhoff type

KW - p-biharmonic

KW - Variational method

UR - https://www.scopus.com/pages/publications/85068848647

U2 - 10.1186/s13661-019-1237-6

DO - 10.1186/s13661-019-1237-6

M3 - Article

AN - SCOPUS:85068848647

SN - 1687-2762

VL - 2019

JO - Boundary Value Problems

JF - Boundary Value Problems

IS - 1

M1 - 125

ER -

Existence of nontrivial weak solutions for p-biharmonic Kirchhoff-type equations

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Keywords

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