Principal spectral curves for Lane-Emden fully nonlinear type systems and applications

被引：4

作者：

dos Santos, Ederson Moreira ^{[1
]}

Nornberg, Gabrielle ^{[2
]}

Schiera, Delia ^{[3
,4
,5
]}

Tavares, Hugo ^{[4
,5
]}

机构：

[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Ave Trabalhador Sao Carlense 400 Ctr, BR-13566590 Sao Carlos, SP, Brazil

[2] Univ Chile, Dept Ingn Matemat, Beauchef 851, Santiago, Chile

[3] Univ Studi Campania L Vanvitelli, Dipartimento Matemat & Fis, Viale A Lincoln 5, I-81100 Caserta, Italy

[4] Univ Lisbon, CAMGSD, Inst Super Tecn, Ave Rovisco Pais, P-1049001 Lisbon, Portugal

[5] Univ Lisbon, Math Dept, Inst Super Tecn, Ave Rovisco Pais, P-1049001 Lisbon, Portugal

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 62卷 / 02期

关键词：

35D35; 35D40; 35J47; 35P30; 35B50; ANTI-MAXIMUM PRINCIPLE; ELLIPTIC-EQUATIONS; VISCOSITY SOLUTIONS; POSITIVE SOLUTIONS; EIGENVALUES; EXISTENCE; BOUNDARY; REGULARITY; UNIQUENESS; GROWTH;

D O I：

10.1007/s00526-022-02386-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we exploit the phenomenon of two principal half eigenvalues in the context of fully nonlinear Lane-Emden type systems with possibly unbounded coefficients and weights. We show that this gives rise to the existence of two principal spectral curves on the plane. We develop an anti-maximum principle, which is a novelty even for Lane-Emden systems involving the Laplacian operator. As applications, we derive a maximum principle in small domains for these systems, as well as existence and uniqueness of positive solutions in the sublinear regime. Most of our results are new even in the scalar case, in particular for a class of Isaac's operators with unbounded coefficients, whose W2,e regularity estimates we also prove.

引用

页数：38

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