Existence and multiplicity of positive solutions to a class of quasilinear elliptic equations in N

Tsing San Hsu

doi:10.1155/2010/579387

Existence and multiplicity of positive solutions to a class of quasilinear elliptic equations in N

Tsing San Hsu^*

^*Corresponding author for this work

Center for General Education

Research output: Contribution to journal › Journal Article › peer-review

Abstract

We consider the following class of quasilinear elliptic equations h ^pδ_pu + V_ε(x) | u | ^p-2 u = | u | ^q-2 u, u (x) > 0 for all x εR^N, where h > 0, δ_pu = div (| u | p - 2 u), 2 ≤ p < N, p < q < p < * = N p / (N - p). We allow the potential V_ε to be unbounded below and prove the existence and multiplicity for positive solutions.

Original language	English
Article number	579387
Journal	Boundary Value Problems
Volume	2010
DOIs	https://doi.org/10.1155/2010/579387
State	Published - 2010

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title = "Existence and multiplicity of positive solutions to a class of quasilinear elliptic equations in N",

abstract = "We consider the following class of quasilinear elliptic equations h pδpu + Vε(x) | u | p-2 u = | u | q-2 u, u (x) > 0 for all x εRN, where h > 0, δpu = div (| u | p - 2 u), 2 ≤ p < N, p < q < p < * = N p / (N - p). We allow the potential Vε to be unbounded below and prove the existence and multiplicity for positive solutions.",

author = "Hsu, \{Tsing San\}",

year = "2010",

doi = "10.1155/2010/579387",

language = "英语",

volume = "2010",

journal = "Boundary Value Problems",

issn = "1687-2762",

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N2 - We consider the following class of quasilinear elliptic equations h pδpu + Vε(x) | u | p-2 u = | u | q-2 u, u (x) > 0 for all x εRN, where h > 0, δpu = div (| u | p - 2 u), 2 ≤ p < N, p < q < p < * = N p / (N - p). We allow the potential Vε to be unbounded below and prove the existence and multiplicity for positive solutions.

AB - We consider the following class of quasilinear elliptic equations h pδpu + Vε(x) | u | p-2 u = | u | q-2 u, u (x) > 0 for all x εRN, where h > 0, δpu = div (| u | p - 2 u), 2 ≤ p < N, p < q < p < * = N p / (N - p). We allow the potential Vε to be unbounded below and prove the existence and multiplicity for positive solutions.

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U2 - 10.1155/2010/579387

DO - 10.1155/2010/579387

M3 - 文章

AN - SCOPUS:77951452750

SN - 1687-2762

VL - 2010

JO - Boundary Value Problems

JF - Boundary Value Problems

M1 - 579387

ER -

Existence and multiplicity of positive solutions to a class of quasilinear elliptic equations in N

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