Infinitely many nodal solutions for a class of quasilinear elliptic equations

摘要

In this paper, we study the existence of infinitely many nodal solutions for the following quasilinear elliptic equation @@@ {-del center dot[phi'(vertical bar del i vertical bar(2))del u] + vertical bar u vertical bar(alpha-2)u = f(x), x is an element of R-N, @@@ u(x) -> 0, as vertical bar x vertical bar -> infinity, @@@ where N >= 2, phi(t) behaves like t(q/2) for small t and t(p/2) for large t, 1 < p < q < N, f is an element of C-1 (R+, R) is of subcritical, q <= alpha <= p*q'/p', let p* = Np/N -> p', p' and q' be the conjugate exponents respectively of p and q. For any given integer k >= 0, we prove that the equation has a pair of radial nodal solution with exactly k nodes.

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