Maximum principles and nonexistence results for radial solutions to equations involving p-Laplacian

被引：5

作者：

Adamowicz, Tomasz ^{[2
]}

Katamajska, Agnieszka ^{[1
]}

机构：

[1] Warsaw Univ, Inst Math, PL-02097 Warsaw, Poland

[2] Univ Cincinnati, Dept Math Sci, Cincinnati, OH 45221 USA

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2010年 / 33卷 / 13期

关键词：

maximum principles; radial solutions; p-Laplace equation; singular elliptic PDEs; DIFFERENTIAL-EQUATIONS; OSCILLATION; BIFURCATION; SYMMETRY;

D O I：

10.1002/mma.1280

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain the variant of maximum principle for radial solutions of, possibly singular, p-harmonic equations of the form -a(vertical bar x vertical bar)Delta(p()w) + h (vertical bar x vertical bar, w, del w(x) . x/vertical bar x vertical bar) = phi(w), as well as for solutions of the related ODE. We show that for the considered class of equations local maxima of vertical bar w vertical bar form a monotone sequence in vertical bar x vertical bar and constant sign solutions are monotone. The results are applied to nonexistence and nonlinear eigenvalue problems. We generalize our previous work for the case h equivalent to 0. Copyright (C) 2010 John Wiley & Sons, Ltd.

引用

页码：1618 / 1627

页数：10

共 50 条

[21] Radial symmetry for positive solutions of fractional p-Laplacian equations via constrained minimization method [J].

Xie, Liuliu ;

Huang, Xiaotao ;

Wang, Lihe .

APPLIED MATHEMATICS AND COMPUTATION, 2018, 337 :54-62

[22] Existence of Sign-Changing Solutions to Equations Involving the One-Dimensional p-Laplacian [J].

Ma, Ruyun ;

Jiang, Lingfang .

JOURNAL OF APPLIED MATHEMATICS, 2014,

[23] Radial solutions to critical elliptic systems involving p-Laplacian and different Hardy-type terms [J].

Kang, Dongsheng .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 526 (01)

[24] Multiple solutions of a p-Laplacian model involving a fractional derivative [J].

Liu, Xiping ;

Jia, Mei ;

Ge, Weigao .

ADVANCES IN DIFFERENCE EQUATIONS, 2013,

[25] Multiple solutions for nonhomogeneous Schrodinger-Kirchhoff type equations involving the fractional p-Laplacian in RN [J].

Pucci, Patrizia ;

Xiang, Mingqi ;

Zhang, Binlin .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 54 (03) :2785-2806

[26] Symmetry and monotonicity of positive solutions for Choquard equations involving a generalized tempered fractional p-Laplacian in Rn [J].

Fan, Linlin ;

Cao, Linfen ;

Zhao, Peibiao .

FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2023, 26 (06) :2757-2773

[27] Existence of Nontrivial Solutions for Fractional Differential Equations with p-Laplacian [J].

Zhang, Li ;

Wang, Fanglei ;

Ru, Yuanfang .

JOURNAL OF FUNCTION SPACES, 2019, 2019

[28] Symmetry of positive solutions for Choquard equations with fractional p-Laplacian [J].

Ma, Lingwei ;

Zhang, Zhenqiu .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 182 :248-262

[29] Existence of positive radial solutions for the n-dimensional p-Laplacian [J].

Ercole, G ;

Zumpano, A .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 44 (03) :355-360

[30] The p-Laplacian equation with superlinear and supercritical growth, multiplicity of radial solutions [J].

Bognár, G ;

Drábek, P .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 60 (04) :719-728

← 1 2 3 4 5 →