Multiplicity of Solution for a Quasilinear Equation with Singular Nonlinearity

Kaushik Bal; Prashanta Garain

doi:10.1007/s00009-020-01515-5

Multiplicity of Solution for a Quasilinear Equation with Singular Nonlinearity

Kaushik Bal, Prashanta Garain

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

13 Scopus citations

Abstract

For an open, bounded domain Ω in R^N which is strictly convex with smooth boundary, we show that there exists a Λ > 0 such that for 0 < λ< Λ , the quasilinear singular problem -Δpu=λu-δ+uqinΩu=0on∂Ω;u>0inΩadmits at least two distinct solutions u and v in Wloc1,p(Ω)∩L∞(Ω) provided δ≥ 1 , 2N+2N+2<p<N and p-1<q<NpN-p-1.

Original language	English
Article number	91
Journal	Mediterranean Journal of Mathematics
Volume	17
Issue number	3
DOIs	https://doi.org/10.1007/s00009-020-01515-5
State	Published - 1 Jun 2020
Externally published	Yes

Keywords

Quasilinear problem
a priori estimates
singular nonlinearity
topological degree

ASJC Scopus subject areas

General Mathematics

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10.1007/s00009-020-01515-5

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title = "Multiplicity of Solution for a Quasilinear Equation with Singular Nonlinearity",

abstract = "For an open, bounded domain Ω in RN which is strictly convex with smooth boundary, we show that there exists a Λ > 0 such that for 0 < λ< Λ , the quasilinear singular problem -Δpu=λu-δ+uqinΩu=0on∂Ω;u>0inΩadmits at least two distinct solutions u and v in Wloc1,p(Ω)∩L∞(Ω) provided δ≥ 1 , 2N+2N+2",

keywords = "Quasilinear problem, a priori estimates, singular nonlinearity, topological degree",

author = "Kaushik Bal and Prashanta Garain",

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year = "2020",

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doi = "10.1007/s00009-020-01515-5",

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T1 - Multiplicity of Solution for a Quasilinear Equation with Singular Nonlinearity

AU - Bal, Kaushik

AU - Garain, Prashanta

PY - 2020/6/1

Y1 - 2020/6/1

N2 - For an open, bounded domain Ω in RN which is strictly convex with smooth boundary, we show that there exists a Λ > 0 such that for 0 < λ< Λ , the quasilinear singular problem -Δpu=λu-δ+uqinΩu=0on∂Ω;u>0inΩadmits at least two distinct solutions u and v in Wloc1,p(Ω)∩L∞(Ω) provided δ≥ 1 , 2N+2N+2

AB - For an open, bounded domain Ω in RN which is strictly convex with smooth boundary, we show that there exists a Λ > 0 such that for 0 < λ< Λ , the quasilinear singular problem -Δpu=λu-δ+uqinΩu=0on∂Ω;u>0inΩadmits at least two distinct solutions u and v in Wloc1,p(Ω)∩L∞(Ω) provided δ≥ 1 , 2N+2N+2

KW - Quasilinear problem

KW - a priori estimates

KW - singular nonlinearity

KW - topological degree

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DO - 10.1007/s00009-020-01515-5

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JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 3

M1 - 91

ER -

Multiplicity of Solution for a Quasilinear Equation with Singular Nonlinearity

Abstract

Keywords

ASJC Scopus subject areas

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