Soliton solutions to Kirchhoff type problems involving the critical growth in

Liang, Sihua; Shi, Shaoyun

doi:10.1016/j.na.2012.12.003

Cited by 86 publications

(39 citation statements)

References 29 publications

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“…There are some recent papers on the Kirchhoff type of problem involving critical exponent, see [21,1,7,11,8]. In particular, in [1], Alves, Corrêa, and Figueiredo have studied the existence of solutions for equations…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Multiple positive solutions for Kirchhoff type of problems with singularity and critical exponents

Lei

Liao

Tang

2015

Journal of Mathematical Analysis and Applications

108

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Multiple positive solutions for Kirchhoff type of problems with singularity and critical exponents

Lei

Liao

Tang

2015

Journal of Mathematical Analysis and Applications

108

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“…In [3] it is shown existence of solution for f subcritical and critical. Multiplicity of solutions were showed in [11], [14], [19], [27], [28] and [29] using genus or category theory. The case in which the Laplace operator is replaced by the p-Laplacian or the p(x)-Laplacian has been considered in [6] and [5] respectively.…”

Section: Introductionmentioning

confidence: 99%

Study of a nonlinear Kirchhoff equation with non-homogeneous material

Figueiredo

Júnior

Suárez

2014

Journal of Mathematical Analysis and Applications

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“…Essentially, Kirchhoff's model takes into account the changes in the length of the string produced by transverse vibrations. For recent results in this direction, we refer the reader, eg, to previous studies …”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Fractional magnetic Schrödinger‐Kirchhoff problems with convolution and critical nonlinearities

Liang

Repovš

Zhang

2020

Math Methods in App Sciences

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In this paper, we are concerned with the existence and multiplicity of solutions for the fractional Choquard‐type Schrödinger‐Kirchhoff equations with electromagnetic fields and critical nonlinearity: ε2sMfalse(false[ufalse]s,A2false)false(−normalΔfalse)Asu+Vfalse(xfalse)u=false(false|x|−α∗Ffalse(false|u|2false)false)ffalse(false|u|2false)u+false|u|2s∗−2u,.5emx∈RN,ufalse(xfalse)→0,.5emas.5emfalse|xfalse|→∞, where false(−normalΔfalse)As is the fractional magnetic operator with 00 is a positive parameter. The electric potential V∈Cfalse(RN,double-struckR0+false) satisfies V(x)=0 in some region of RN, which means that this is the critical frequency case. We first prove the (PS)c condition, by using the fractional version of the concentration compactness principle. Then, applying also the mountain pass theorem and the genus theory, we obtain the existence and multiplicity of semiclassical states for the above problem. The main feature of our problems is that the Kirchhoff term M can vanish at zero.

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Soliton solutions to Kirchhoff type problems involving the critical growth in

Cited by 86 publications

References 29 publications

Multiple positive solutions for Kirchhoff type of problems with singularity and critical exponents

Multiple positive solutions for Kirchhoff type of problems with singularity and critical exponents

Study of a nonlinear Kirchhoff equation with non-homogeneous material

Fractional magnetic Schrödinger‐Kirchhoff problems with convolution and critical nonlinearities

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