Nonlocal τ(m)$$ \tau (m) $$‐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.