20.500.12556/RUL-146300 Existence and multiplicity of solutions involving the $p(x)$-Laplacian equations on the effect of two nonlocal terms We 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. p(x)-Laplacian operator variational methods Kirchhoff problem bi-nonlocal term Ambrosetti-Rabinowitz condition true false true Angleški jezik Ni določen Založnikova različica članka je v RUL shranjena v skladu z založnikovo pogodbo z avtorji. (Datum opombe: 24. 5. 2023) Članek v reviji 2023-05-23 12:18:09 2023-05-23 12:18:12 2025-08-08 13:22:22 0000-00-00 00:00:00 2023 0 0 Str. 1452-1467 no. 6 Vol. 16 Jun. 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.956 1937-1632 10.3934/dcdss.2022129 111490051 Clanek_155.pdf Clanek_155.pdf 1 1553FDE0188E088B508DD7900633BFF7 63f7d0abc39bda72ae9110bcc3ddb19375f2be359839037c609ab8cbc38cf0f2 c193ee4f-f953-11ed-a314-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=169459 https://www.aimsciences.org/article/doi/10.3934/dcdss.2022129 1 d970abe6-f952-11ed-a314-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=169458 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0