Existence of a Sigh-Changing Solution Result for Logarithmic Schrödinger Equations with Weight Function

This paper is devoted to studying the existence of solutions for the following logarithmic Schrödinger problem: −div(a(x)∇u)+V(x)u=ulogu2+k(x)| u |q1−2u+h(x)| u |q2−2u, x∈ℝN.(1)We first prove that the corresponding functional I belongs to C1(HV1(ℝN),ℝ). Furthermore, by using the variational method, we prove the existence of a sigh-changing solution to problem (1).

Thoughts on Present Situation of Development of Rural Animal Husbandry and Its Relationship with Construction of Ecological Agriculture and Revitalization of Rural Industry

After several rounds of phased ups and downs of development,rural animal husbandry finally presents a shrinking and depressed development situation under the comprehensive action of the failure of transformation and upgrading and the increasing production costs and breeding risks.Actively exploring and guiding the healthy and sound development of rural animal husbandry is not only an important measure to promote the construction of ecological agriculture,but also the main starting point to realize the revitalization of rural industry.This paper analyzes the present situation of the development of rural animal husbandry in recent years,the influence of animal husbandry on the construction of ecological agriculture and the revitalization of rural industry,and puts forward the corresponding measures,in order to promote the steady and efficient development of animal husbandry in the grand strategy of revitalizing rural industry.

EXISTENCE OF MULTIPLE SOLUTIONS FOR A FRACTIONAL p-LAPLACIAN SYSTEM WITH CONCAVE-CONVEX TERM

In this article, we study the existence of multiple solutions for the following sys-tem driven by a nonlocal integro-differential operator with zero Dirichlet boundary conditions {（-△）p^su=a（x）｜u｜^q-2u＋2α/α＋βc（x）｜u｜^α-2u｜u｜^β,in Ω,（-△）p^su=a（x）｜u｜^q-2u＋2α/α＋βc（x）｜u｜^α｜u｜^β-2.inΩ,（0.1）u=v=0,in R^n／Ωwhere Ω is a smooth bounded domain in R^n, n 〉 ps with s ∈ （0, 1） fixed, a（x）, b（x）, c（x） 〉 0and a（x）,b（x）,c（x） ∈ L^∞（Ω）, 1 〈 q 〈 p and α,β 〉 1 satisfy p 〈 α＋β 〈 p^＊, p^＊ = np/n-ps·By Nehari manifold and fibering maps with proper conditions, we obtain the multiplicity ofsolutions to problem （0.1）.

Warm temperature compromises JA-regulated basal resistance to enhance Magnaporthe oryzae infection in rice

Changes in global temperatures profoundly affect the occurrence of plant diseases.It is well known that rice blast can easily become epidemic in relatively warm weather.However,the molecular mechanism remains unclear.In this study,we show that enhanced blast development at a warm temperature(22C)compared with the normal growth temperature(28C)is rice plant-determined.Comparative transcriptome analysis revealed that jasmonic acid(JA)biosynthesis and signaling genes in rice could be effectively induced by Magnaporthe oryzae at 28C but not at 22C.Phenotypic analyses of the osaoc1 and osmyc2 mutants,OsCOI1 RNAi lines,and OsMYC2-OE plants further demonstrated that compromised M.oryzaeinduced JA biosynthesis and signaling lead to enhanced blast susceptibility at the warm temperature.Consistent with these results,we found that exogenous application of methyl jasmonate served as an effective strategy for improving blast resistance under the warm environmental conditions.Furthermore,decreased activation of JA signaling resulted in the downregulated expression of some key basal resistance genes at 22C when compared with 28C.Among these affected genes,OsCEBiP(chitin elicitorbinding protein precursor)was found to be directly regulated by OsMYB22 and its interacting protein OsMYC2,a key component of JA signaling,and this contributed to temperature-modulated blast resistance.Taken together,these results suggest that warm temperature compromises basal resistance in rice and enhances M.oryzae infection by reducing JA biosynthesis and signaling,providing potential new strategies for managing rice blast disease under warm climate conditions.