NORMALIZED SOLUTIONS FOR THE GENERAL KIRCHHOFF TYPE EQUATIONS

In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈ℝ×H^(1)(ℝ^(N))to the general Kirchhoff problem-M\left(\int_{\mathbb{R}^N}\vert\nabla u\vert^2{\rm d}x\right)\Delta u+\lambda u=g(u)~\hbox{in}~\mathbb{R}^N,u\in H^1(\mathbb{R}^N),N\geq 1,satisfying the normalization constraint\int_{\mathbb{R}^N}u^2{\rm d}x=c,where M∈C([0,∞))is a given function satisfying some suitable assumptions.Our argument is not by the classical variational method,but by a global branch approach developed by Jeanjean et al.[J Math Pures Appl,2024,183:44–75]and a direct correspondence,so we can handle in a unified way the nonlinearities g(s),which are either mass subcritical,mass critical or mass supercritical.

Yap methylation-induced FGL1 expression suppresses anti-tumor immunity and promotes tumor progression in KRAS-driven lung adenocarcinoma

Background:Despite significant strides in lung cancer immunotherapy,the response rates for Kirsten rat sarcoma viral oncogene homolog(KRAS)-driven lung adenocarcinoma(LUAD)patients remain limited.Fibrinogen-like protein 1(FGL1)is a newly identified immune checkpoint target,and the study of related resistance mechanisms is crucial for improving the treatment outcomes of LUAD patients.This study aimed to elucidate the potential mechanism by which FGL1 regulates the tumor microenvironment in KRAS-mutated cancer.Methods:The expression levels of FGL1 and SET1 histone methyltransferase(SET1A)in lung cancer were assessed using public databases and clinical sam-ples.Lentiviruses were constructed for transduction to overexpress or silence FGL1 in lung cancer cells and mouse models.The effects of FGL1 and Yes-associated protein(Yap)on the immunoreactivity of cytotoxic T cells in tumor tissues were evaluated using immunofluorescence staining and flow cytometry.Chromatin immunoprecipitation and dual luciferase reporter assays were used to study the SET1A-directed transcriptional program.Results:Upregulation of FGL1 expression in KRAS-mutated cancer was inversely correlated with the infiltration of CD8^(+)T cells.Mechanistically,KRAS activated extracellular signal-regulated kinase 1/2(ERK1/2),which subsequently phosphorylated SET1A and increased its stability and nuclear localization.SET1A-mediated methylation of Yap led to Yap sequestration in the nucleus,thereby promoting Yap-induced transcription of FGL1 and immune evasion in KRAS-driven LUAD.Notably,dual blockade of programmed cell death-1(PD-1)and FGL1 further increased the therapeutic efficacy of anti-PD-1 immunotherapy in LUAD patients.Conclusion:FGL1 could be used as a diagnostic biomarker of KRAS-mutated lung cancer,and targeting the Yap-FGL1 axis could increase the efficacy of anti-PD-1 immunotherapy.