Bifurcation and blow-up results for equations with p-Laplacian and convex-concave nonlinearity

被引：0
作者：
Ilyasov, Yavdat Shavkatovich [1 ]
机构：
[1] Russian Acad Sci, Ufa Sci Ctr, Inst Math, 112 Chernyshevsky Str, Ufa 450008, Russia
来源：
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS | 2017年 / 96期
关键词：
concave-convex nonlinearity; Collatz-Wielandt formula; p-Laplacian; bifurcation; blow up; 2ND-ORDER ELLIPTIC-OPERATORS; PRINCIPAL EIGENVALUE; POSITIVE SOLUTIONS; MAXIMUM PRINCIPLE; REGULARITY; EXISTENCE;
D O I：
10.14232/ejqtde.2017.1.96
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with the existence of global, blow-up and bifurcation solutions for parametrized families of elliptic and parabolic equations with p-Laplacian and concave-convex nonlinearity. The main results are obtained by means of a generalised Collatz-Wielandt formula.
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页码：1 / 13
页数：13
相关论文
共 42 条
[21]   VARIATIONAL FORMULA FOR PRINCIPAL EIGENVALUE FOR OPERATORS WITH MAXIMUM PRINCIPLE [J].
DONSKER, MD ;
VARADHAN, SRS .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1975, 72 (03) :780-783
[22]  
Escobedo M., 1999, Rend. Mat. Appl., V19, P211
[23]  
Hewitt Edwin, 1969, Real and Abstract Analysis. A Modern Treatment of the Theory of Functions of a Real Variable
[24]   On nonlocal existence results for elliptic equations with convex-concave nonlinearities [J].
Il'yasov, Y .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 61 (1-2) :211-236
[25]   On positive solutions of indefinite elliptic equations [J].
Il'Yasov, Y .
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2001, 333 (06) :533-538
[26]  
Il'yasov Y., 2017, BRANCHES POSITIVE SO
[27]   Bifurcation calculus by the extended functional method [J].
Il'yasov, Ya. Sh. .
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2007, 41 (01) :18-30
[28]   A duality principle corresponding to the parabolic equations [J].
Il'yasov, Yavdat .
PHYSICA D-NONLINEAR PHENOMENA, 2008, 237 (05) :692-698
[29]   Computation of maximal turning points to nonlinear equations by nonsmooth optimization [J].
Il'yasov, Yavdat ;
Ivanov, Aleksandr .
OPTIMIZATION METHODS & SOFTWARE, 2016, 31 (01) :1-23
[30]   On global positive solutions of parabolic equations with a sign-indefinite nonlinearity [J].
Il'yasov, YS .
DIFFERENTIAL EQUATIONS, 2005, 41 (04) :548-556
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