The aim of this paper is to examine the existence of at least two distinct nontrivial solutions to a Schrödinger-type problem involving the nonlocal fractional $p(\cdot )$ p ( ⋅ ) -Laplacian with concave–convex nonlinearities when, in general, the nonlinear term does not satisfy the Ambrosetti–Rabinowitz condition. The main tools for obtaining this result are the mountain pass theorem and a modified version of Ekeland’s variational principle for an energy functional with the compactness condition of the Palais–Smale type, namely the Cerami condition. Also we discuss several existence results of a sequence of infinitely many solutions to our problem. To achieve these results, we employ the fountain theorem and the dual fountain theorem as main tools.

The extensive isolation of genes responsive to hyperthermal stress conditions in soft coral (Scleronephthya gracillimum) is described. Soft coral colonies were exposed to high seawater temperature conditions. Gene candidates whose transcript levels changed in response to hyperthermal conditions were identified by differential display polymerase chain reaction (DD-PCR). Twenty-four types of candidate genes were identified, 18 of which were upregulated in expression and 6 of which were downregulated. The genes were found to function in post-translational modification, protein turnover and chaperones (O); translation, ribosomal structure and biogenesis (J); signal transduction mechanisms (T); defense mechanisms (V); inorganic ion transport and metabolism (P); energy production and conversion (C); cytoskeleton (Z); cell cycle control, cell division and chromosome partitioning (D); lipid transport and metabolism (I); chromatin structure and dynamics (B); transcription (K); replication, recombination and repair (L); secondary metabolites biosynthesis, transport and catabolism (Q); extracellular structures (W); general function prediction (R); and finally, unknown function (S) based on KOG classification. Among these candidates, their expressional changes were confirmed by real-time quantitative PCR (qRT-PCR). These 24 isolated gene candidates were differentially expressed and therefore have great potential as molecular biomarkers for the identification of environmental stressors.

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