High perturbations of critical fractional Kirchhoff equations with logarithmic nonlinearity

This paper deals with the study of combined effects of logarithmic and critical nonlinearities for the following class of fractional p-Kirchhoff equations: {M([u](s,p)(p))(-Delta)(p)(s)u = lambda vertical bar u vertical bar(q-2)u ln vertical bar u vertical bar(2) + vertical bar u vertical bar p(s)*(-2)u in Omega, u = 0 in R-N \ Omega, where Omega subset of R-N is a bounded domain with Lipschitz boundary, N > sp with s is an element of (0, 1), p >= 2, p*s = Np/(N - ps) is the fractional critical Sobolev exponent, and lambda is a positive parameter. The main result establishes the existence of nontrivial solutions in the case of high perturbations of the logarithmic nonlinearity (large values of lambda). The features of this paper are the following: (i) the presence of a logarithmic nonlinearity; (ii) the lack of compactness due to the critical term; (iii) our analysis includes the degenerate case, which corresponds to the Kirchhoff term M vanishing at zero. (c) 2021 Elsevier Ltd. All rights reserved.