## Topological Methods in Nonlinear Analysis

### On solutions of semilinear elliptic equation with linear growth nonlinearity in $\mathbb{R}^N$

#### Abstract

We study nontrivial solutions for a class of semilinear elliptic equation which could be resonant at infinity. We establish the existence of solutions for the equation by considering the modified non-resonant problem associated with the original equation through Morse theory. Moreover, only linear growth assumption is imposed on the nonlinearity and condition on the potential is weaker than the coercive assumption.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 46, Number 1 (2015), 45-56.

Dates
First available in Project Euclid: 30 March 2016

https://projecteuclid.org/euclid.tmna/1459343884

Digital Object Identifier
doi:10.12775/TMNA.2015.036

Mathematical Reviews number (MathSciNet)
MR3443677

Zentralblatt MATH identifier
1371.35108

#### Citation

Cheng, Rong; Hu, Jianhua. On solutions of semilinear elliptic equation with linear growth nonlinearity in $\mathbb{R}^N$. Topol. Methods Nonlinear Anal. 46 (2015), no. 1, 45--56. doi:10.12775/TMNA.2015.036. https://projecteuclid.org/euclid.tmna/1459343884

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