Multiplicity of concentrating solutions for a class of fractional Kirchhoff equation View Full Text


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Article Info

DATE

2019-01

AUTHORS

Xiaoming He, Wenming Zou

ABSTRACT

We study the multiplicity of concentrating solutions to the nonlinear fractional Kirchhoff equation ε2sa+ε4s-3b∫R3|(-Δ)s2u|2dx(-Δ)su+V(x)u=f(u)inR3,where ε>0 is a positive parameter, (-Δ)s is the fractional laplacian with s∈(34,1),a,b are positive constants, and V is a positive potential such that inf∂ΛV>infΛV for some open bounded subset Λ⊂R3. We relate the number of positive solutions with the topology of the set where V attains its minimum in Λ. The proof is based on the Ljusternik–Schnirelmann theory. More... »

PAGES

159-203

References to SciGraph publications

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    http://scigraph.springernature.com/pub.10.1007/s00229-018-1017-0

    DOI

    http://dx.doi.org/10.1007/s00229-018-1017-0

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    https://app.dimensions.ai/details/publication/pub.1101386682


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