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)

引用

页数：22

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