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AbstractIn this paper, we study the nonexistence of stable solutions for the quasilinear Schrödinger equation 0.1−Δu−[Δ(1+u2)1/2]u2(1+u2)1/2=h(x)|u|q−1u,x∈RN,$$ -\Delta u- \bigl[\Delta\bigl(1+u^{2}\bigr)^{1/2} \bigr]\frac{ u}{2(1+u^{2})^{1/2}}=h(x) \vert u \vert ^{q-1}u,\quad x\in R^{N}, $$ where N≥3$N\ge3$,… Click to show full abstract
AbstractIn this paper, we study the nonexistence of stable solutions for the quasilinear Schrödinger equation 0.1−Δu−[Δ(1+u2)1/2]u2(1+u2)1/2=h(x)|u|q−1u,x∈RN,$$ -\Delta u- \bigl[\Delta\bigl(1+u^{2}\bigr)^{1/2} \bigr]\frac{ u}{2(1+u^{2})^{1/2}}=h(x) \vert u \vert ^{q-1}u,\quad x\in R^{N}, $$ where N≥3$N\ge3$, q≥5/2$q\ge5/2$ and the function h(x)$h(x)$ is continuous and positive in RN$R^{N}$. Under suitable assumptions on h(x)$h(x)$ and q, we prove that Eq. (0.1) has no nonnegative and stable solutions.
Journal Title: Boundary Value Problems
Year Published: 2018
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