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- W3185204690 abstract "<p style='text-indent:20px;'>This paper is concerned with the existence and multiplicity of constant sign solutions for the following fully nonlinear equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=FE1> begin{document}$ begin{equation*} left{ begin{array}{l} -mathcal{M}_mathcal{C}^{pm}(D^2u) = mu f(u) text{in} Omega, u = 0 text{on} partialOmega, end{array} right. end{equation*} $end{document} </tex-math> </disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id=M3>begin{document}$ Omegasubsetmathbb{R}^N $end{document}</tex-math></inline-formula> is a bounded regular domain with <inline-formula><tex-math id=M4>begin{document}$ Ngeq3 $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=M5>begin{document}$ mathcal{M}_mathcal{C}^{pm} $end{document}</tex-math></inline-formula> are general Hamilton-Jacobi-Bellman operators, <inline-formula><tex-math id=M6>begin{document}$ mu $end{document}</tex-math></inline-formula> is a real parameter. By using bifurcation theory, we determine the range of parameter <inline-formula><tex-math id=M7>begin{document}$ mu $end{document}</tex-math></inline-formula> of the above problem which has one or multiple constant sign solutions according to the behaviors of <inline-formula><tex-math id=M8>begin{document}$ f $end{document}</tex-math></inline-formula> at <inline-formula><tex-math id=M9>begin{document}$ 0 $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=M10>begin{document}$ infty $end{document}</tex-math></inline-formula>, and whether <inline-formula><tex-math id=M11>begin{document}$ f $end{document}</tex-math></inline-formula> satisfies the signum condition <inline-formula><tex-math id=M12>begin{document}$ f(s)s>0 $end{document}</tex-math></inline-formula> for <inline-formula><tex-math id=M13>begin{document}$ sneq0 $end{document}</tex-math></inline-formula>.</p>" @default.
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- W3185204690 date "2021-01-01" @default.
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- W3185204690 title "Existence and multiplicity for Hamilton-Jacobi-Bellman equation" @default.
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- W3185204690 doi "https://doi.org/10.3934/cpaa.2021130" @default.
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