Multiplicity of Solution for a Quasilinear Equation with Singular Nonlinearity

Kaushik Bal; Prashanta Garain

doi:10.1007/s00009-020-01523-5

Multiplicity of Solution for a Quasilinear Equation with Singular Nonlinearity

Kaushik Bal, Prashanta Garain

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

5 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<N(p-1)N-p.

Original language	English
Article number	100
Journal	Mediterranean Journal of Mathematics
Volume	17
Issue number	4
DOIs	https://doi.org/10.1007/s00009-020-01523-5
State	Published - 1 Aug 2020
Externally published	Yes

Keywords

Quasilinear problem
a priori estimates
singular nonlinearity
topological degree

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s00009-020-01523-5

Cite this

@article{3fbf7a0de49549c68cd470d1d18453ac,

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",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.",

year = "2020",

month = aug,

day = "1",

doi = "10.1007/s00009-020-01523-5",

language = "English",

volume = "17",

journal = "Mediterranean Journal of Mathematics",

issn = "1660-5446",

publisher = "Birkhauser Verlag Basel",

number = "4",

}

TY - JOUR

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

AU - Bal, Kaushik

AU - Garain, Prashanta

PY - 2020/8/1

Y1 - 2020/8/1

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

UR - http://www.scopus.com/inward/record.url?scp=85088911516&partnerID=8YFLogxK

U2 - 10.1007/s00009-020-01523-5

DO - 10.1007/s00009-020-01523-5

M3 - Article

AN - SCOPUS:85088911516

SN - 1660-5446

VL - 17

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 4

M1 - 100

ER -

Multiplicity of Solution for a Quasilinear Equation with Singular Nonlinearity

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this