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Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 12
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Articles

Singularly perturbed quasilinear Schrödinger equations with negative parameters

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Pages 2239-2251 | Received 24 Jan 2018, Accepted 18 Mar 2018, Published online: 08 Apr 2018
 

ABSTRACT

We consider a class of quasilinear Schrödinger equations of the form -ε2div(g2(u)u)+ε2g(u)g(u)|u|2+V(x)u=f(u),xRN,

where g2(u)=1+κu22(1+u2),κ(-2,0) and N3. By variational methods, we construct a solution uε which concentrates, as ε0, around the local minima of the potential V(x). One of our contributions is that we give the expression of some constant in our main result.

AMS SUBJECT CLASSIFICATIONS:

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Supported by NSFC [grant number 11371146]; the Fundamental Research Funds for the Central Universities [grant number 2015zz133].

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