Electron. J. Differential Equations,
Vol. 2019 (2019), No. 111, pp. 124.
Existence of positive solutions for systems of nonlinear
SturmLiouville differential equations with weight functions
Jinfang He, Lu Yang
Abstract:
This article concerns the existence of componentwise positive solutions for
systems of nonlinear SturmLiouville differential equations with weight
functions, in which one nonlinear term is uniformly superlinear or
uniformly sublinear, and the other is locally uniformly superlinear
or locally uniformly sublinear. As applications, we consider the
existence of global componentwise positive solutions to the corresponding
nonlinear eigenvalue problem with respect to positive parameters.
The discussion is based on the product formula of fixed point index on
product cone, the fixed point index theory in cones and LeraySchauder
degree theory.
Submitted March 24, 2019. Published September 26, 2019.
Math Subject Classifications: 34B18, 47H11, 47N20.
Key Words: Positive solution; nonlinear eigenvalue problem; fixed point;
strict lower and upper solutions; LeraySchauder degree.
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Jinfang He
School of Mathematics and Statistics
Lanzhou University
Lanzhou, 730000, China
email: hejf14@lzu.edu.cn


Lu Yang
School of Mathematics and Statistics
Lanzhou University
Lanzhou, 730000, China
email: yanglu@lzu.edu.cn

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