Existence and multiplicity of solutions involving the $p(x)$-Laplacian equationsHamdani, Mohamed Karim (Avtor) Mbarki, Lamine (Avtor) Allaoui, Mostafa (Avtor) Darhouche, Omar (Avtor) Repovš, Dušan (Avtor) p(x)-Laplacian operatorvariational methodsKirchhoff problembi-nonlocal termAmbrosetti-Rabinowitz conditionWe study a class of $p(x)$-Kirchhoff problems which is seldom studied because the nonlinearity has nonstandard growth and contains a bi-nonlocal term. Based on variational methods, especially the Mountain pass theorem and Ekeland's variational principle, we obtain the existence of two nontrivial solutions for the problem under certain assumptions. We also apply the Symmetric mountain pass theorem and Clarke's theorem to establish the existence of infinitely many solutions. Our results generalize and extend several existing results.20232023-05-23 12:18:09Članek v reviji146300slZaložnikova različica članka je v RUL shranjena v skladu z založnikovo pogodbo z avtorji. (Datum opombe: 24. 5. 2023)