
The aim of this paper is to study the existence of nodal radial solutions for the \(p(x)\)-Laplacian equation of the form \[ \begin{gathered} -\text{div}(|\nabla |^{p(x)-2}\nabla u)+ a(x)|u|^{p(x)-2} u=|u|^{q(x)- 2} u\quad\text{in }\Omega,\\ u\in W^{1,p(x)}_0(\Omega).\end{gathered}\tag{1} \] Using a variational method, the authors prove that, for any given nonnegative integer \(k\), the equation (1) has a pair of solutions which has exactly \(k\) nodes.
Variational methods for higher-order elliptic equations, \(p(x)\)-Laplacian equation, Degenerate elliptic equations, Variational principles in infinite-dimensional spaces, radially symmetric solution, node
Variational methods for higher-order elliptic equations, \(p(x)\)-Laplacian equation, Degenerate elliptic equations, Variational principles in infinite-dimensional spaces, radially symmetric solution, node
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