On a sublinear Robin equations involving \(\mu (x)\)-Laplacian with small perturbation

The present paper deals with the existence of solutions for Robin equations with variable exponents. In particular, we suppose that the nonlinear part in the equation has an Ekeland’s structure. However, we do not assume any growth condition for the perturbation data. Moreover, using variational arguments, we establish the existence of at least one nontrivial weak solution. This paper extends the recent works established by Bahrouni (Adv Nonlinear Stud 307(20):663-674 2020); (Topol. Methods Nonlinear Anal. https://api.semanticscholar.org/CorpusID:237843657 2021).