Infinitely many solutions of a class of quasilinear elliptic equations in \(\mathbb{R}^N\) with \(p\)-concave and convex nonlinearities. (Chinese. English summary) Zbl 0972.35044

Liu, Shibo; Fan, Xianling

J. Lanzhou Univ., Nat. Sci. 36, No. 5, 10-16 (2000).

Summary: Under proper conditions, we obtain the existence of infinitely many solutions of the following quasilinear elliptic equation \[ -\text{div}(|\nabla u|^{p- 2}\nabla u)+ a(x)|u|^{p- 2}u= h(x)|u|^{q-2} u+\lambda|u|^{s- 2}u,\;u\in W^{1,p}(\mathbb{R}^N), \] where \(p< N\), \(1< q< p< s< p^*\equiv Np/(N- p)\).

MSC:

35J70	Degenerate elliptic equations
35A15	Variational methods applied to PDEs
35A05	General existence and uniqueness theorems (PDE) (MSC2000)
35B33	Critical exponents in context of PDEs

Keywords:

\(p\)-Laplacian equations; critical points; existence