On critical double phase Choquard problems with singular nonlinearity.

In this article, we consider the following double phase problem with singular term and convolution term where & OHM; is a bounded domain in RN with Lipschitz boundary partial differential & OHM;, & gamma; & ISIN; (0, 1), 1 < p < q < q*& mu;, - increment p & phi; = div(| backward difference & phi;|p-2 backward difference & phi;), with p & ISIN; {p, q}, is the homogeneous p-Laplacian. & lambda; > 0 is a real parameter, 0 < & mu; < N, N > p and q*& mu; = (pN - p & mu;/2)/(N - p) is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality. The existence of at least one weak solution is obtained for the above problem by using the Nehari manifold approach.& COPY; 2023 Elsevier B.V. All rights reserved.