NODAL SOLUTIONS FOR A SUPERCRITICAL PROBLEM WITH VARIABLE EXPONENT AND LOGARITHMIC NONLINEARITY

We study the existence of sign-changing solutions for the following supercritical problem with variable exponent and logarithmic nonlinearity {-Delta u = vertical bar u vertical bar(2* -2)u( ln(tau + vertical bar u vertical bar))(vertical bar x vertical bar beta) in B-1, u = 0 on partial derivative B-1, where B-1 is the unit ball in R-N, N = 3, 2* = 2N/(N - 2) is the critical Sobolev exponent, and tau >= 1, beta > 0 are constants. For any k is an element of N, if tau >= 1 and 0 < beta < (N - 2)/2, we show that there exist one pair of solutions which change sign exactly k times by variational methods.