scholarly journals Multiplicity of positive solutions to boundary blow-up elliptic problems with sign-changing weights

2011 ◽  
Vol 261 (7) ◽  
pp. 1775-1798 ◽  
Author(s):  
Jorge García-Melián
Keyword(s):  
Positive Solutions ◽  
Blow Up ◽  
Elliptic Problems ◽  
Multiplicity Of Positive Solutions

scholarly journals Positive Solutions for Elliptic Problems with the Nonlinearity Containing Singularity and Hardy-Sobolev Exponents

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yong-Yi Lan ◽  
Xian Hu ◽  
Bi-Yun Tang
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Elliptic Problems ◽  
Semilinear Elliptic Equations ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic ◽  
Multiplicity Of Positive Solutions

In this paper, we study multiplicity of positive solutions for a class of semilinear elliptic equations with the nonlinearity containing singularity and Hardy-Sobolev exponents. Using variational methods, we establish the existence and multiplicity of positive solutions for the problem.

scholarly journals On the Elliptic Problems Involving Multisingular Inverse Square Potentials and Concave-Convex Nonlinearities

2011 ◽  
Vol 2011 ◽  
pp. 1-22
Author(s):  
Tsing-San Hsu
Keyword(s):  
Variational Method ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Elliptic Problems ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Hardy Type ◽  
Multiplicity Of Positive Solutions ◽  
Inverse Square Potentials

A semilinear elliptic problem with concave-convex nonlinearities and multiple Hardy-type terms is considered. By means of a variational method, we establish the existence and multiplicity of positive solutions for problem .

scholarly journals Multiplicity of positive solutions to semi-linear elliptic problems on metric graphs

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Masataka Shibata
Keyword(s):  
Positive Solution ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Existence Result ◽  
Elliptic Problems ◽  
Positive Parameter ◽  
Metric Graphs ◽  
Multiplicity Of Positive Solutions

<p style='text-indent:20px;'>We consider positive solutions of semi-linear elliptic equations</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ - \epsilon^2 u'' +u = u^p $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>on compact metric graphs, where <inline-formula><tex-math id="M1">\begin{document}$ p \in (1,\infty) $\end{document}</tex-math></inline-formula> is a given constant and <inline-formula><tex-math id="M2">\begin{document}$ \epsilon $\end{document}</tex-math></inline-formula> is a positive parameter. We focus on the multiplicity of positive solutions for sufficiently small <inline-formula><tex-math id="M3">\begin{document}$ \epsilon $\end{document}</tex-math></inline-formula>. For each edge of the graph, we construct a positive solution which concentrates some point on the edge if <inline-formula><tex-math id="M4">\begin{document}$ \epsilon $\end{document}</tex-math></inline-formula> is sufficiently small. Moreover, we give the existence result of solutions which concentrate inner vertices of the graph.</p>

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