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- W2313634757 abstract "Motivated by some nonlinear models recently arising in Micro-Electro-Mechanical System (MEMS)and new progress on one-dimensional mean curvature type problems,we investigate the existence and exact numbers of positive solutionsfor a class of boundary value problems with $varphi$-Laplacian$$ -(varphi(u'))'=lambda f(u); on (-L, L),quad u(-L)=u(L)=0,$$when the parameters $lambda$ and $L$ vary.Various exact multiplicity results as well as global bifurcation diagrams are obtained.These results include the applicationsto one-dimensional MEMS equations with fringing field as well asmean curvature type problems.We also extend and improve one of the main results of Korman and Li[Proc. Roy. Soc. Edinburgh Sect. A, 140(6):1197--1215, 2010] (Theorem 3.4).With the aid of numerical simulations, we find many interesting newexamples, which reveal the striking complexity of bifurcation patterns for the problem." @default.
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- W2313634757 date "2015-01-01" @default.
- W2313634757 modified "2023-09-24" @default.
- W2313634757 title "On the existence of positive solutions for some nonlinear boundary value problems and applications to MEMS models" @default.
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- W2313634757 doi "https://doi.org/10.3934/dcds.2015.35.3627" @default.
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