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On the existence of least energy solution for Kirchhoff equation in R 3
Author(s) -
Hu Tingxi,
Lu Lu
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6216
Subject(s) - mathematics , energy (signal processing) , mathematical analysis , mathematical physics , type (biology) , combinatorics , statistics , ecology , biology
We are concerned with the following Kirchhoff‐type equation:− a + b ∫R 3| ∇ u | 2 d x Δ u +h ∞ + h ( x ) u = ( q ∞ + q ( x ) ) | u | p − 2 u inR 3 , where a , b > 0 are constants,h ∞ , q ∞ > 0 , 2 < p < 6 , and h ( x ) , q ( x ) are positive functions inC 2 ( R 3 ) satisfying h ( x ) ↘ 0 , q ( x ) ↘ 0 as | x | → ∞ . Under certain assumptions on h ( x ) , q ( x ) andh ∞ , q ∞ , we prove the existence of least energy solution for the aforementioned Kirchhoff‐type equation.