Electron. J. Differential Equations, Vol. 2020 (2020), No. 99, pp. 1-14.

Asymptotically linear and superlinear elliptic equations with gradient terms

Yuanhong Wei, Jian Tian

Abstract:
In this article we establish the existence of solutions for elliptic problem involving a gradient term. To handle the so-called non-variational problem, we use a variational methods. We assume that the nonlinear term satisfies an asymptotically linear growth condition or a superlinear growth condition. We show the existence of at least one positive solution and one negative solution.

Submitted March 9, 2020. Published September 23, 2020.
Math Subject Classifications: 35B09, 35J20, 35A01.
Key Words: Positive solution; nonlinearity; gradient term; iterative method; mountain pass theorem.

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Yuanhong Wei
School of Mathematics
Jilin University
130012, Changchun, China
email: weiyuanhong@jlu.edu.cn
Jian Tian
School of Mathematics
Jilin University
130012, Changchun, China
email: tianjian@jlu.edu.cn

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