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2020 Generalized limit theorem and bifurcation for problems with Pucci's operator
Guowei Dai
Topol. Methods Nonlinear Anal. 56(1): 229-261 (2020). DOI: 10.12775/TMNA.2020.012

Abstract

We establish a new limiting result which extends the famous Whyburn's limit theorem. As applications, we study the existence and multiplicity of one-sign or sign-changing solutions with a prescribed number of simple zeros for the following problem \begin{equation*} \begin{cases} -\mathcal{M}_{\lambda,\Lambda}^+\left(D^2 u\right)=\mu f(u) &\text{in } \Omega,\\ u=0&\text{on } \partial\Omega, \end{cases} \end{equation*} where $\mathcal{M}_{\lambda,\Lambda}^+$ denotes the Pucci extremal operator. Combining bifurcation approach with our generalized limit theorem, we determine the range of parameter $\mu$ in which the above problem has one or multiple one-sign or sign-changing solutions according to the behaviors of $f$ at $0$ and $\infty$, and whether $f$ satisfies the signum condition $f(s)s> 0$ for $s\neq0$.

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Guowei Dai. "Generalized limit theorem and bifurcation for problems with Pucci's operator." Topol. Methods Nonlinear Anal. 56 (1) 229 - 261, 2020. https://doi.org/10.12775/TMNA.2020.012

Information

Published: 2020
First available in Project Euclid: 10 September 2020

MathSciNet: MR4175078
Digital Object Identifier: 10.12775/TMNA.2020.012

Rights: Copyright © 2020 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.56 • No. 1 • 2020
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