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^*

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摘要

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.

原文	英語
文章編號	579387
期刊	Boundary Value Problems
卷	2010
DOIs	https://doi.org/10.1155/2010/579387
出版狀態	已出版 - 2010

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10.1155/2010/579387

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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.",

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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

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