Twin positive solutions for singular nonlinear elliptic equations
Keywords
Singular nonlinearity, positive solutions, variational methods, truncation techniques, upper-lower solutionsAbstract
For a bounded domain $Z\subseteq{\mathbb{R}}^N$ with a $C^2$-boundary, we prove the existence of an ordered pair of smooth positive strong solutions for the nonlinear Dirichlet problem $$ -\Delta_p x(z) = \beta(z)x(z)^{-\eta}+f(z,x(z)) \quad \text{a.e on } Z \text{ with } x\in W^{1,p}_0(Z), $$ which exhibits the combined effects of a singular term ($\eta\geq 0$) and a $(p-1)$-linear term $f(z,x)$ near $+\infty$, by using a combination of variational methods, with upper-lower solutions and with suitable truncation techniques.Downloads
Published
2010-04-23
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1.
CHEN, Jianqing, PAPAGEORGIOU, Nikolaos S. and ROCHA, Eugénio M. Twin positive solutions for singular nonlinear elliptic equations. Topological Methods in Nonlinear Analysis. Online. 23 April 2010. Vol. 35, no. 1, pp. 187 - 201. [Accessed 8 October 2024].
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