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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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",

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journal = "Boundary Value Problems",

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

Abstract

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