A nonexistence result for a class of quasilinear Schr\"{o}dinger equations with Berestycki-Lions conditions

Jianhua Chen, Yubo He


In this paper, we study the following quasilinear Schr\"{o}dinger equation
-\Delta u+V(x)u-[\Delta(1+u^2)^{1/2}]\frac{u}{2(1+u^2)^{1/2}}=h(u),\,\, x\in\R^N,
where $N\geq3$, $2^*=\frac{2N}{N-2}$, $V(x)$ is a potential function. Unlike $V\in\mathcal{C}^2(\R^N)$, we only need to assume that $V\in\mathcal{C}^1(\R^N)$.
By using a change
of variable, we prove the non-existence of ground state solutions with Berestycki-Lions conditions, which contain the superliner case:
and asymptotically linear case:
Our results extend and complement the results in related literature.


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