In the present paper, we study normalized solutions for following quasilinear Schr\"odinger equations: $$-\Delta u-u\Delta u^2+\lambda u=|u|^{p-2}u \quad \text{in}~\mathbb R^N,$$ with prescribed mass $$\int_{\mathbb R^N} u^2=a^2.$$ We first consider mass-supercritical case $p>4+\frac{4}{N}$, which has not been studied before. By using a perturbation method, succeed to prove existence of ground ...

In this paper, we obtain results of nonexistence nonconstant positive solutions, and also existence an unbounded sequence sign-changing solutions for some critical problems involving conformally invariant operators on the unit sphere, in particular to fractional Laplacian operator Euclidean space. Our arguments are based a reduction initial problem space equivalent standard sphere vice versa, w...