Nonlocal τ(m)‐Laplacian‐like problem with logarithmic nonlinearity and without Ambrosetti–Rabinowitz condition on compact Riemannian manifolds

Abstract

By means of variational methods, we study the existence and multiplicity of nontrivial weak solutions for a nonlocal ‐Laplacian‐like problem, arising from a capillarity phenomenon, with logarithmic nonlinearity and without the Ambrosetti–Rabinwitz condition, in the setting of variable exponents of Sobolev spaces in compact Riemannian manifolds.