Infinitely many solutions to quasilinear Schrödinger equations with critical exponent

This paper is concerned with the following quasilinear Schrödinger equations with critical exponent: −∆pu + V(x)|u| p−2u − ∆p(|u| 2ω)|u| 2ω−2u = ak(x)|u| q−2u + b|u| 2ωp ∗−2u, x ∈ R N. Here ∆pu = div(|∇u| p−2∇u) is the p-Laplacian operator with 1 < p < N, p N p N−p is the critical Sobolev exponent. 1 ≤ 2ω < q < 2ωp, a and b are suitable positive parameters, V ∈ C(RN, [0, ∞)), k ∈ C(RN, R). With the help of the concentration-compactness principle and R. Kajikiya’s new version of symmetric Mountain Pass Lemma, we obtain infinitely many solutions which tend to zero under mild assumptions on V and k

Infinitely many solutions to quasilinear Schrödinger equations with critical exponent

This paper is concerned with the following quasilinear Schrödinger equations with critical exponent: \begin{equation*}\label{eqS0.1} - \Delta _p u+ V(x)|u|^{p-2}u - \Delta _p(|u|^{2\omega}) |u|^{2\omega-2}u = a k(x)|u|^{q-2}u+b |u|^{2\omega p^{*}-2}u,\qquad x\in\mathbb{R}^N. \end{equation*} Here $\Delta _p u =\mathrm{div}(|\nabla u|^{p-2}\nabla u)$ is the $p$-Laplacian operator with $1< p < N$, $p^* =\frac{Np}{N-p}$ is the critical Sobolev exponent. $1\le 2\omega<q<2\omega p,$ $a$ and $b$ are suitable positive parameters, $V \in C(\mathbb{R}^N, [0, \infty) ),$ $k\in C(\mathbb{R}^N,\mathbb{R})$. With the help of the concentration-compactness principle and R. Kajikiya's new version of symmetric Mountain Pass Lemma, we obtain infinitely many solutions which tend to zero under mild assumptions on $V$ and $k$

Ground state solutions for a quasilinear Schrodinger equation with singular coefficients

In this article, we study the quasilinear Schrodinger equation with the critical exponent and singular coefficients, $$-\Delta u +V(x)u-\Delta(|u|^2)u=\lambda\frac{|u|^{q-2}u}{|x|^{\mu}} +\frac{|u|^{22^*(\nu)-2}u}{|x|^\nu}\quad\text{in } \mathbb{R}^N,$$ where $N\geq 3$, $2<q<22^*(\mu)$, $2^*(s)=\frac{2(N-s)}{N-2}$, and $\lambda, \mu, \nu$ are parameters with $\lambda>0$, $\mu, \nu \in [0,2)$. By applying the Mountain Pass Theorem and the Concentration Compactness Principle, we establish the existence of the ground state solutions to the above problem

Classical Signaling and Trans-Signaling Pathways Stimulated by Megalobrama amblycephala IL-6 and IL-6R

Interleukin-6 (IL-6) is a multipotent cytokine. IL-6 plays a dual role in inflammation through both classical signaling (IL-6 binds membrane IL-6 receptor/IL-6R) and trans-signaling (IL-6 binds soluble IL-6R). However, the regulation of IL-6 activity, especially the regulation of signaling pathways and downstream genes mediated by IL-6 trans-signaling, remains largely unclear in teleost. Grass carp (Ctenopharyngodon idellus) hepatic (L8824) cells, kidney (CIK) cells, and primary hepatocytes were used as test models in this study. First, the biological activity of recombinant blunt snout bream (Megalobrama amblycephala) IL-6 (rmaIL-6) and sIL-6R (rmasIL-6R) was verified by quantitative PCR (qPCR) and western blot. The western blot results showed that rmaIL-6 significantly upregulated signal transducer and activator of transcription 3 (STAT3) phosphorylation in L8824 cells and primary hepatocytes, while rmaIL-6 in combination with rmasIL-6R (rmaIL-6+rmasIL-6R) significantly upregulated STAT3 phosphorylation in all types of cells. Furthermore, maIL-6 and maIL-6+rmasIL-6R could only induce extracellular-signal-regulated kinase 1/2 (ERK1/2) phosphorylation in L8824 cells and CIK cells, respectively. Therefore, IL-6 mainly acts by activating the janus kinase (JAK)/STAT3 pathway rather than the mitogen-activated protein kinase (MEK)/ERK pathway. Finally, the activation of the JAK2/STAT3 pathway was shown to be essential for the generation of socs3a and socs3b induced by IL-6 trans-signaling after treatment by JAK2/STAT3 pathway inhibitors (c188-9 and TG101348). These findings provide functional insights into IL-6 classical signaling and trans-signaling regulatory mechanisms in teleost, enriching our knowledge of fish immunology

Effects of Different Sulfur Compounds on the Distribution Characteristics of Subcellular Lead Content in <i>Arabis alpina</i> L. var. <i>parviflora</i> Franch under Lead Stress

Sulfur plays a vital role in the phytoremediation of lead-contaminated soil. The effects of different sulfur forms (S Na2S, and Na2SO4) on lead (Pb) absorption in hyperaccumulator Arabis alpina L. var. parviflora Franch were studied in a soil pot experiment. The subcellular sulfur and lead enrichment characteristics in A. alpina were studied by adding sulfur in different forms and concentrations (0, 75, and 150 mg·kg−1) to Pb-contaminated soil. The results show that the root and shoot biomass increased by 1.94 times under Na2S and Na2SO4 treatment, and the root–shoot ratio of A. alpina increased 1.62 times under the three forms of sulfur treatments, compared with the control. Sulfur content in cell walls and soluble fractions of the root and shoot of A. alpina significantly increased 3.35~5.75 times and decreased 5.85 and 9.28 times in the organelles under 150 mg·kg−1 Na2SO4 treatment. Meanwhile, Pb content in the root and shoot cell walls of A. alpina significantly increased by 3.54 and 2.75 times, respectively. Pb content in the shoot soluble fraction increased by 3.46 times, while it significantly reduced by 3.78 times in the shoot organelle. Pb content in the root organelle and soluble fraction decreased by 2.72 and 2.46 times. Different forms and concentrations of sulfur had no regularity in the effect of Pb and sulfur content in the subcellular components of A. alpina, but the bioconcentration and translocation factors of A. alpina increased compared with the control. Under different concentrations of Na2SO4, there was a significant positive correlation between the contents of sulfur and Pb in the subcellular components of the root of A. alpina (p A. alpina by strengthening the cell wall fixation and vacuolar compartmentalization

Characteristics of heavy metal accumulation in five wild plants in Huize Lead-Zinc mining area

In order to screen out the plants used to repair heavy metal pollution in the soil, five plants and surface soil were collected in the Huize lead-zinc mine area, centered on the hyperaccumulator plant Arabis alpina L. var. parviflora Franch, measured the heavy metal content of in shoot and root of plant and surface soil, and analyzed the characteristics of heavy metal accumulation in plants. The results showed that the soil Cd pollution in the Huize lead-zinc mining area was the most serious; among the five plants, the Cd bioconcentration factor(BCF) and translocation factor(TF) of A. alpina were more than 1, and the TF of Pb was more than 1; the TF of Anaphalis margaritacea, Cyananthus inflatus and Arenaria orbiculata to Cu and Zn were more than 1, the TF of Juncus effusus to Cd and Zn were more than 1. These five plants had good tolerance to heavy metals and were of great significance to the remediation and restoration of heavy metal contaminated soil in lead-zinc mining areas

Functional characterization of two corticotropin-releasing hormone receptors in Larimichthys crocea

In the neuroendocrine system, corticotropin-releasing hormone (CRH) plays an important role in the hypothalamic–pituitary–adrenal/interrenal (HPA/HPI) axis. It exerts its effects by activating CRHRs, which belong to the class B G protein-coupled receptor family. Two characteristic genes of CRHR1 subtypes in the Larimichthys crocea genome were identified: LcCRHR1-1 and LcCRHR1-2. Alignments indicated that they were highly homologous to known and validated teleost CRHR1s. The CDS sequences of the two receptors were cloned into the pEGFP-N1 plasmid, and membrane localization of the fusion expressing LcCRHR1-1-EGFP and LcCRHR1-2-EGFP was revealed in HEK293 cells. Treatment with LcCRH could lead to two receptors internalization and trigger a significant increase in the secondary messenger cAMP and Ca2+ and mitogen-activated protein kinase phosphorylation in an LcCRH dose-dependent manner. Based on quantitative real-time PCR, LcCRHR1s were expressed in all examined tissues and highly expressed in the brain and ovaries. Furthermore, immunohistochemical findings showed the specific localization of CRHR1s in ovarian follicle cells. Collectively, our study identified two CRH receptors in L. crocea and suggested that the CRH/CRHR1 system is potentially involved in the neuroendocrine regulation of reproduction in this marine fish

Effects of a root-colonized dark septate endophyte on the glutathione metabolism in maize plants under cadmium stress

A high Cd-tolerant dark septate endophyte (DSE), Exophiala pisciphila, was inoculated into maize (Zea mays L.) roots under Cd stress. The Cd content, enzymes activity and thiol compound content relevant to glutathione (GSH) metabolism in maize leaves were analyzed. The Cd content in maize shoots increased with increasing Cd stress, but the DSE significantly reduced the Cd content at the 40 mg/kg Cd treatment. Cd stress increased the enzyme activity of glutathione reductase (GR), glutathione S-transferase (GST) and glutathione peroxidase (GSH-Px) as well as the thiol compound contents of sulfur, thiols (-SH) and oxidized glutathione (GSSG). The content of reduced GSH and the GSH/GSSG ratio reached a peak at the 5 mg/kg Cd treatment but then decreased with increasing Cd stress. Furthermore, the DSE significantly enhanced the GR and GSH-Px activity and increased the contents of -SH and GSH under low Cd stress (5 and 10 mg/kg), but decreased the γ-glutamylcysteine synthetase and GST activity under high Cd stress (20 and 40 mg/kg). Highly positive correlations between the Cd content with enzymes activity and enzymes activity with thiol compound content were observed. Results indicated that DSE played a role in activating GSH metabolism in maize leaves under Cd stress

Species diversity of Arabis alpina L. communities in two Pb/Zn mining areas with different smelting history in Yunnan Province, China

In order to explore the species compositions and species diversity (Dominance (Do), Shannon-Wiener index (H0), Simpson diversity index (Dsi), Species richness (DMG), Pielou evenness index (Epi) and Fre- quency (Fr)) of twenty Arabis alpina L. var. parviflora Franch communities, field investigation was con- ducted in Huize county, Yunnan province, China. Some 20 A. alpina communities were distributed in two traditional smelting tailing piles of Minbingyingjiying (TST) and Shangduoduo village (SDD) with different Pb smelting history. The morphological characteristics (plant height, branch number, basal leaf length, basal leaf width and root morphology) of A. alpina, contents and accumulation characteristics of eight potentially toxic metals (As, Cd, Cr, Cu, Pb, Zn, Al, Fe) in soil and plants were analyzed. The results showed that the morphological characteristics of A. alpina were mean plant height 12.25 cm, the basal leaf length 17.69 cm, leaf width 5.40 cm, the total root length 117.86 cm plant 1, the root diameter 0.90 mm. The leaves of A. alpina in SDD were longer and narrower with higher plant height compared with in TST. The main companion plants of A. alpina were Sporobolus fertilis (Steud.) W. D. Clayt, Arenaria orbiculata Royle ex Edgew. et Hook. F. and Eulalia speciosa. (Debeaux). The H0 and Dsi were 0.56e2.04 and 0.44e0.95, respectively. The plant species numbers, H’, Dsi and Epi of A. alpina communities in TST were higher than those in SDD. Pb contents in shoot of two A. alpina samples were more than 1000 mg kg 1, Cd content in shoot of one A. alpina sample >100 mg kg 1 and Zn contents in shoot of seven A. alpina samples >10,000 mg kg 1 with the enrichment factors and transport coefficients greater than 1. The results indicate that A. alpina as a Zn, Pb and Cd hyperaccumulator, could be used for long-term phy- toremediation of soils contaminated by Cd, Pb and Zn. Species diversity of A. alpina community during long-term natural vegetation restoration was high in the middle succession with single-peak model, and A. alpina would be dominant in the succession climax stage in potentially toxic metal contamination areas