Zhang, XiaZhang, ChaoGao, Huimin2022-01-042022-01-042018-01-19Zhang, X., Zhang, C., & Gao, H. (2018). Solutions for p(x)-Laplace equations with critical frequency. <i>Electronic Journal of Differential Equations, 2018</i>(31), pp. 1-20.1072-6691https://hdl.handle.net/10877/15087This article concerns the p(x)-Laplace equations with critical frequency -div(|∇u|p(x)-2∇u) + V(x)|u|p(x)-2u = ƒ(x, u) in ℝN, where 1 < p- ≤ p(x) ≤ p+ < N. We study this equation with the potentials being zero. By using variational method, we obtain the existence of nonnegative solutions. Moreover, if ƒ(x, t) is odd in t, for any m ∈ ℕ we derive m pairs of nontrivial solutions.Text20 pages1 file (.pdf)enAttribution 4.0 InternationalVariable exponent spacep(x)-LaplaceCritical frequencyWeak solutionArticle