On a concave-convex elliptic problem with a nonlinear boundary condition

被引：6

作者：

Ramos Quoirin, Humberto ^{[1
]}

Umezu, Kenichiro ^{[2
]}

机构：

[1] Univ Santiago Chile, Casilla 307,Correo 2, Santiago, Chile

[2] Ibaraki Univ, Dept Math, Fac Educ, Mito, Ibaraki 3108512, Japan

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2016年 / 195卷 / 06期

关键词：

Semilinear elliptic problem; Concave-convex nonlinearity; Nonlinear boundary condition; Positive solution; Bifurcation; Super and subsolutions; Nehari manifold; NEHARI MANIFOLD; EQUATION; BIFURCATION;

D O I：

10.1007/s10231-015-0531-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate an indefinite superlinear elliptic equation coupled with a sublinear Neumann boundary condition (depending on a positive parameter ), which provides a concave-convex nature to the problem. We establish a global multiplicity result for positive solutions in the spirit of Ambrosetti-Brezis-Cerami and obtain their asymptotic profiles as . Furthermore, we also analyse the case where the nonlinearity is concave. Our arguments are based on a bifurcation analysis, a comparison principle, and variational techniques.

引用

页码：1833 / 1863

页数：31

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