Existence and Concentration Results for the General Kirchhoff-Type Equations

被引：4
|
作者：
Deng, Yinbin [1 ]
Shuai, Wei [1 ]
Zhong, Xuexiu [2 ]
机构：
[1] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China
[2] South China Normal Univ, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou 510631, Peoples R China
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2023年 / 33卷 / 03期
关键词：
Kirchhoff-type equations; Semiclassical solutions; Topologically stable critical points; NONLINEAR SCHRODINGER-EQUATIONS; SEMICLASSICAL BOUND-STATES; STANDING WAVES; POSITIVE SOLUTIONS; CRITICAL FREQUENCY; ELLIPTIC PROBLEMS; CRITICAL-POINTS; PEAK SOLUTIONS; SADDLE-POINTS; MULTI-BUMP;
D O I：
10.1007/s12220-022-01145-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the following singularly perturbed Kirchhoff-type equations ? ? ? -epsilon 2M epsilon 2-N RN |Vu|2dx ?u + V(x)u = |u|p-2u in RN, u E H1(RN), N >_ 1, where M E C([0, oo)) and V E C(RN) are given functions. Under very mild assumptions on M, we prove the existence of single-peak or multi-peak solution u epsilon for above problem, concentrating around topologically stable critical points of V, by a direct corresponding argument. This gives an affirmative answer to an open problem raised by Figueiredo et al. (Arch Ration Mech Anal 213(3):931-979, 2014)
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页数：22
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