Global bifurcation curves for fourth-order MEMS/NEMS models II

2024/12/24 by Lin, Manting, Pan, Hongjing
#34B18 #34C23 #74G35 #74K10 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2412.18427

Abstract

Global solution curve and exact multiplicity of positive solutions for a class of fourth-order beam equations with clamped boundary conditions are derived. The results extend atheorem of P. Korman (2004) by allowing the presence of a singularity in the nonlinearity. The paper also establishes an a priori estimate for C³-norm of positive solutions, which is optimal in Holder regularity. Applications to MEMS/NEMS models are presented.

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