On an Anisotropic Logistic Equation

被引:0
作者
Gasinski, Leszek [1 ]
Papageorgiou, Nikolaos S. [2 ,3 ]
机构
[1] Univ Natl Educ Commiss, Dept Math, Podchorazych 2, PL-30084 Krakow, Poland
[2] Natl Tech Univ Athens, Dept Math, Zografou Campus, Athens 15780, Greece
[3] Univ Craiova, Dept Math, Craiova 200585, Romania
关键词
anisotropic operator; equidiffusive logistic reaction; uniqueness; minimal positive solution; anisotropic regularity; DEGENERATE ELLIPTIC EQUATION; POSITIVE SOLUTIONS;
D O I
10.3390/math12091280
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider a nonlinear Dirichlet problem driven by the (p(z),q)-Laplacian and with a logistic reaction of the equidiffusive type. Under a nonlinearity condition on a quotient map, we show existence and uniqueness of positive solutions and the result is global in parameter lambda. If the monotonicity condition on the quotient map is not true, we can no longer guarantee uniqueness, but we can show the existence of a minimal solution u(lambda)* and establish the monotonicity of the map lambda bar right arrow u(lambda)* and its asymptotic behaviour as the parameter lambda decreases to the critical value (lambda(1)) over cap (q) > 0 (the principal eigenvalue of (-Delta(q),W-0(1,q)(Omega))).
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页数:13
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