Home » Pub-Topic: Partial Differential Equations, Pub-Type: Articles in International Journals

PAPER: Twin positive solutions for singular nonlinear elliptic equations

REF. DATE:9 March 2010 CREATED/MODIFIED: 14 January 2016 297 views No Comment

Twin positive solutions for singular nonlinear elliptic equations (with J. Chen, N.S. Papageorgiou), Topological Methods in Nonlinear Analysis 35:1(2010), 187-201.


ABSTRACT: For a bounded domain \Omega\subseteq\bkR^N with a C^2-boundary, we prove the existence of an ordered pair of smooth positive strong solutions for the nonlinear Dirichlet problem

    \[-\Delta_p\, u(x) = \beta(x)u(x)^{-\eta}+f(x,u(x)) \mbox{ a.e. on } \Omega \quad\mbox{with } u\in W^{1,p}_0(\Omega),\]

which exhibits the combined effects of a singular term (\eta\geq 0) and a (p-1)-linear term f(x,u) near +\infty, by using a combination of variational methods, with upper-lower solutions and with suitable truncation techniques.


Download: Preprint version (RIA | download) / Publisher version (TMNA)
Remark: The paper follows Papageorgiou’s notation
Extra info: (P067/2010-03-01)

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