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Existence of positive solutions to perturbed nonlinear Dirichlet problems involving critical growth

dc.contributor.authorZhang, Huixing ( )
dc.contributor.authorZhang, Ran ( )
dc.date.accessioned2022-03-30T18:55:33Z
dc.date.available2022-03-30T18:55:33Z
dc.date.issued2017-02-21
dc.identifier.citationZhang, H., & Zhang, R. (2017). Existence of positive solutions to perturbed nonlinear Dirichlet problems involving critical growth. Electronic Journal of Differential Equations, 2017(54), pp. 1-11.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/15580
dc.description.abstract

We consider the following perturbed nonlinear elliptic problem with critical growth

-ε2 ∆u + V(x)u = ƒ(x)|u|p-2u + α/α+β K(x)|u|α-2u|v|β, x ∈ ℝN,

-ε2 ∆v + V(x)v = g(x)|v|p-2 v + β/+β K(x)|u|α|v|β-2v, x ∈ ℝN,

u(x), v(x) → 0 as |x| → ∞.

Using variational methods, we prove the existence of positive solutions.
dc.formatText
dc.format.extent11 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectPerturbed nonlinear Dirichlet problemen_US
dc.subjectCritical growthen_US
dc.subjectPalais-Smale conditionen_US
dc.subjectVariational methodsen_US
dc.titleExistence of positive solutions to perturbed nonlinear Dirichlet problems involving critical growthen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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