TY - JOUR AU - Hu, Jianhua AU - Cheng, Rong PY - 2015/09/01 Y2 - 2024/03/28 TI - On solutions of semilinear elliptic equation with linear growth nonlinearity in $\mathbb{R}^{N}$ JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 46 IS - 1 SE - DO - 10.12775/TMNA.2015.036 UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2015.036 SP - 45 - 56 AB - 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. ER -