On critical variable-order Kirchhoff type problems with variable singular exponentZuo, Jiabin (Avtor) Choudhuri, Debajyoti (Avtor) Repovš, Dušan (Avtor) fractional Laplacian of variable-ordercontinuous embeddinggenussymmetric mountain pass theoremvariable singular exponentWe 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.20222022-05-04 12:34:57Članek v reviji136441UDK: 517.956ISSN pri članku: 0022-247XDOI: 10.1016/j.jmaa.2022.126264COBISS_ID: 106082051sl