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

Jianhua Hu, Rong Cheng

DOI: http://dx.doi.org/10.12775/TMNA.2015.036


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.


Critical points; semilinear elliptic equation; Morsetheory

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