20.500.12556/RUL-136441 On critical variable-order Kirchhoff type problems with variable singular exponent We establish a continuous embedding $W^{s(\cdot),2}(\Omega) \hookrightarrow L^{\alpha (\cdot)}(\Omega)$, where the variable exponent $\alpha(x)$ can be close to the critical exponent $2_s^\ast = \frac{2N}{N-2\bar{s}(x)}$, with $\bar{s}(x) = s(x,x)$ for all $x \in \bar{\Omega}$. Subsequently, this continuous embedding is used to prove the multiplicity of solutions for critical nonlocal degenerate Kirchhoff problems with a variable singular exponent. Moreover, we also obtain the uniform $L^\infty$-estimate of these infinite solutions by a bootstrap argument. fractional Laplacian of variable-order continuous embedding genus symmetric mountain pass theorem variable singular exponent true false true Angleški jezik Ni določen Članek v reviji 2022-05-04 12:34:57 2022-05-04 12:35:00 2022-09-19 13:12:06 0000-00-00 00:00:00 2022 0 0 18 str. iss. 1, art. 126264 Vol. 514 Oct. 2022 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.956 0022-247X 10.1016/j.jmaa.2022.126264 106082051 Clanek_133.pdf Clanek_133.pdf 1 E040DF625EDAC44BC6BF9217C1BA08A1 d93fc2f2a402295257f55ad3840900dfa4a10373edafc90b74a0c8c430b6047a d3c420a0-cb95-11ec-8aca-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=156096 https://www.sciencedirect.com/science/article/pii/S0022247X22002785 1 c1cf86a2-cb95-11ec-8aca-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=156095 Pedagoška fakulteta Fakulteta za matematiko in fiziko 0 0 0