On elliptic equations with unbounded or decaying potentials involving Stein-Weiss convolution parts and critical exponential growth

We study a class of nonlinear Schrodinger equations with Stein-Weiss convolution parts -Delta u + V(x)u = (integral(R2) F(u)/vertical bar x - y vertical bar mu parallel to y vertical bar(beta) dy) f(u)/vertical bar x vertical bar(beta), x is an element of R-2, where Vis an unbounded or decaying potential, beta > 0, mu > 0 with 0 < 2 beta+ mu < 2, and Fdenotes the primitive of fthat fulfills the critical exponential growth in the Trudinger-Moser sense at infinity. Via establishing a new version of the Trudinger-Moser inequality, we shall exploit the general minimax principle to demonstrate the existence of nontrivial solutions using variational method. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.