An existence result for a quasilinear degenerate problem in R-N

作者：Stircu Iulia Dorotheea^*

来源：Electronic Journal of Qualitative Theory of Differential Equations, 2017, (5): 1-11.

DOI：10.14232/ejqtde.2017.1.5

• quasilinear degenerate problem
• weak solutions
• nonhomogeneous operator
• mountain pass theorem

In this paper we study an existence result of the quasilinear problem -div [phi'(vertical bar del u vertical bar(2))del u] + a (x) vertical bar u vertical bar(alpha-2)u = vertical bar u vertical bar(gamma-2)u + vertical bar u vertical bar(beta-2)u in R-N (N >= 3), where phi (t) behaves like t(q/2) for small t and t(p/2) for large t, a is a positive potential, 1 < p < q < N, 1 < alpha <= p*q'/p' and max {alpha, q} < gamma < beta < p* = pN/ (N - p), with p' and q' the conjugate exponents of p, respectively q. Our main result is the proof of the existence of a weak solution, based on the mountain pass theorem.

• 出版日期2017