Infinitely many solutions to Kirchhoff double phase problems with variable exponents

In this work we deal with elliptic equations driven by the variable exponent double phase operator with a Kirchhoff term and a right-hand side that is just locally defined in terms of very mild assumptions. Based on an abstract critical point result of Kajikiya (2005) and recent a priori bounds for generalized double phase problems by the authors (2022), we prove the existence of a sequence of nontrivial solutions whose $L^\infty$-norms converge to zero

Cladistic relationships within the genus Cinnamomum (Lauraceae) in Taiwan based on analysis of leaf morphology and inter-simple sequence repeat (ISSR) and internal transcribed spacer (ITS) molecular markers

We examined leaf morphological characteristics, ISSR (inter-simple sequence repeat) genetic polymorphisms and ITS (rDNA internal transcribed spacer) molecular markers in 12 endemic species of Cinnamomum in Taiwan to determine their cladistic relationships. The leaf morphology and ISSR data support the division of the genus into sections Camphora and Cinnamomum. The genetic relationship between Cinnamomum camphora and Cinnamomum micranthum is very close; both species share a specific 11 bp deletion in their ITS sequences. A close relationship between Cinnamomum insularimontanum and Cinnamomum macrostemon was supported by leaf morphology, ISSR and ITS data and the ITS analysis indicates that Cinnamomum subavenium is closely related to these two species. The ITS analysis also indicates that Cinnamomum japonicum, Cinnamomum austrosinense and Cinnamomum reticulatum are closely related. Leaf morphology and ISSRs also support the kinship between C. japonicum and C. austrosinense. The ITS data support a close cluster consisting of C. osmophloeum, C. camphora and C. micranthum, suggesting that Cinnamomum osmophloeum might be a key species in the evolutionary transition from section Camphora to section  Cinnamomum. Our results demonstrate that ISSR and ITS markers can clearly identify the 12 endemic Cinnamomum species in Taiwan.Key words: Cinnamomum, morphology, taxonomy, ISSR (inter-simple sequence repeat), ITS (internal transcribed spacer), phylogeny

Double phase anisotropic variational problems involving critical growth

In this paper, we investigate some existence results for double phase anisotropic variational problems involving critical growth. We first establish a Lions type concentration-compactness principle and its variant at infinity for the solution space, which are our independent interests. By employing these results, we obtain a nontrivial nonnegative solution to problems of generalized concave-convex type. We also obtain infinitely many solutions when the nonlinear term is symmetric. Our results are new even for the $p(\cdot)$-Laplace equations