NONEXISTENCE RESULT TO DOUBLE PHASE PROBLEMS INVOLVING ????????-LAPLACIAN WITH EXPONENTIAL NONLINEARITY

Abstract

In this paper, we consider the instability of weak solutions to the problem

where ∇????=(????1????????1,????2????????2,...,????????????????????),????????,????=1,...,???? satisfy some general hypotheses, ????≥????≥2 and ????,????̃,????∈ ????loc1(ℝ????) are nonnegative functions satisfying some growth conditions at infinity. Our result can be seen as a generalization of that from the Laplace operator to the Δ????-Laplacian. Moreover, our result is also extension of that from the Grushin operator to the Δ????-Laplacian.