Positive radial solutions for multiparameter Dirichlet systems with mean curvature operator in Minkowski space and Lane-Emden type nonlinearities

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Gurban, Daniela¹  Jebelean, Petru¹ 

[1] West Univ Timisoara, Dept Math, Blvd V Parvan 4, Timisoara 300223, Romania

关键词: Minkowski curvature operator;    Lane-Emden nonlinearities;    Positive solution;    Non-existence/existence;    Multiplicity;    Fixed point index;    Lower and upper solutions;   

DOI  :  10.1016/j.jde.2018.10.030

来源: Elsevier

【 摘 要 】

We deal with Dirichlet systems involving the mean curvature operator in Minkowski space M(w) = div(del w/root 1-vertical bar del w vertical bar(2)) in a ball in R-N. Using the fixed point index and the lower and upper solutions method, we first obtain the existence of positive solutions for a class of differential systems with a singular phi-Laplacian, subjected to homogeneous mixed boundary conditions. The main application of the general results concerns Dirichlet systems with Lane-Emden type nonlinearities in a superlinear case, depending on two parameters lambda(1), lambda(2). So, we prove that for such a system there exists a continuous curve Gamma which separates the first quadrant in two disjoint unbounded open sets O-1 and O-2 such that the system has zero, at least one or at least two radial positive solutions, according to (lambda(1), lambda(2)) is an element of O-1 or (lambda(1), lambda(2)) is an element of Gamma or (lambda(1), lambda(2)) is an element of O-2. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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