Ground state sign-changing solutions for a class of double-phase problem in bounded domains

This paper is concerned with the following double-phase problem: {-div(vertical bar del u vertical bar(p-2)del u+a(x)vertical bar del u vertical bar(q-2)del u)=f(x,u) in Omega, u=0 on partial derivative Omega, where N >= 2 and 1 < p < q < N. Assuming that the primitive of f(x,u) is asymptotically q-linear as vertical bar u vertical bar ->infinity and a weak version of Nehari-type monotonicity condition that the function u -> f(x,u)/vertical bar u vertical bar(q-1) is nondecreasing on (-infinity,0)(0,infinity) for a.e. x is an element of Omega, we prove the existence of one ground state sign-changing solution via the constraint variational method and quantitative deformation lemma for the equation. Our results improve and generalize some results obtained by Liu and Dai (J. Differ. Equ. 265(9):4311-4334, 2018).