Quasilinear double phase problem on the whole space

Abstract

In the present paper, we study the existence of a radial sign-changing solution to a class of quasilinear double phase problems in $R^N$. Without assuming the usual strictly increasing condition on $\frac{f(x,t)}{{\left|t\right|}^{q-1}}$, we provide some sufficient conditions under which the above problems have at least one sign-changing radial ground states solution. We generalize the result of Liu and Dai [J. Math. Phys. 61(2020) 091508].