Global bifurcation diagrams and exact multiplicity of positive solutions for a one-dimensional prescribed mean curvature problem arising in MEMS

DOI10.1016/j.na.2013.04.018zbMath1294.34027OpenAlexW1996398511MaRDI QIDQ395409

Yan-Hsiou Cheng, Shin-Hwa Wang, Kuo-Chih Hung

Publication date: 29 January 2014

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2013.04.018

zbMATH Keywords

bifurcationmultiplicity of solutionsboundary eigenvalue problemspositive solutions of nonlinear boundary value problems

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Positive solutions to nonlinear boundary value problems for ordinary differential equations (34B18) Boundary eigenvalue problems for ordinary differential equations (34B09)

Related Items (15)

On the classification and evolution of bifurcation curves for a quasilinear regularized MEMS model ⋮ On the classification and evolution of bifurcation curves for a one-dimensional prescribed curvature problem with nonlinearity \(\exp(\frac{a u}{a + u})\) ⋮ On the evolutionary bifurcation curves for the one-dimensional prescribed mean curvature equation with logistic type ⋮ Ordering properties of positive solutions for a class of \(\varphi\)-Laplacian quasilinear Dirichlet problems ⋮ Some singular equations modeling MEMS ⋮ Bifurcation diagrams and exact multiplicity of positive solutions of one-dimensional prescribed mean curvature equation in Minkowski space ⋮ Time-map analysis to establish the exact number of positive solutions of one-dimensional prescribed mean curvature equations ⋮ Bifurcation results for a class of prescribed mean curvature equations in bounded domains ⋮ A complete classification of bifurcation diagrams for a class of \((p,q)\)-Laplace equations ⋮ A constrained model for MEMS with varying dielectric properties ⋮ Nonexistence of solutions for prescribed mean curvature equations on a ball ⋮ Boundary value problems for a class of first order quasilinear ordinary differential equations ⋮ On the existence of positive solutions for some nonlinear boundary value problems and applications to MEMS models ⋮ Exact multiplicity and bifurcation diagrams of positive solutions of a one-dimensional multiparameter prescribed mean curvature problem ⋮ Applications of total positivity theory to 1D prescribed curvature problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analysis of a one-dimensional prescribed mean curvature equation with singular nonlinearity
• Exact number of solutions of a one-dimensional prescribed mean curvature equation with concave-convex nonlinearities
• Time maps and exact multiplicity results for one-dimensional prescribed mean curvature equations. II
• Time maps and exact multiplicity results for one-dimensional prescribed mean curvature equations
• A note on the nonexistence of solutions for prescribed mean curvature equations on a ball
• Radial solutions for a prescribed mean curvature equation with exponential nonlinearity
• Exact number of solutions of a prescribed mean curvature equation
• Exact multiplicity results for a one-dimensional prescribed mean curvature problem related to MEMS models
• Positive solutions of the Dirichlet problem for the prescribed mean curvature equation
• Classical and non-classical solutions of a prescribed curvature equation
• One-dimensional prescribed mean curvature equation with exponential nonlinearity
• Phase shifts in the collision of massive particles
• Ewald methods for inverse power-law interactions in tridimensional and quasi-two-dimensional systems
• Global solution curves for a class of quasilinear boundary-value problems
• Non-linear effects on canonical MEMS models
• Point Ruptures for a MEMS Equation with Fringing Field
• MULTIPLE POSITIVE SOLUTIONS OF A ONE-DIMENSIONAL PRESCRIBED MEAN CURVATURE PROBLEM
• Nonlinear non-local elliptic equation modelling electrostatic actuation
• Classical and Non-Classical Sign-Changing Solutions of a One-Dimensional Autonomous Prescribed Curvature Equation
• Touchdown and Pull-In Voltage Behavior of a MEMS Device with Varying Dielectric Properties

This page was built for publication: Global bifurcation diagrams and exact multiplicity of positive solutions for a one-dimensional prescribed mean curvature problem arising in MEMS