Geodesic
Multiplicity of solutions for a singular $p$-laplacian elliptic equation
Wen-shu Zhou 1   ; Xiao-dan Wei 1
1 Department of Mathematics Dalian Nationalities University 116600 Dalian, P.R. China
Annales Polonici Mathematici, Tome 99 (2010) no. 2, pp. 157-180 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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The existence of two continuous solutions for a nonlinear singular elliptic equation with natural growth in the gradient is proved for the Dirichlet problem in the unit ball centered at the origin. The first continuous solution is positive and maximal; it is obtained via the regularization method. The second continuous solution is zero at the origin, and follows by considering the corresponding radial ODE and by sub-sup solutions method.
DOI : 10.4064/ap99-2-4
Keywords: existence continuous solutions nonlinear singular elliptic equation natural growth gradient proved dirichlet problem unit ball centered origin first continuous solution positive maximal obtained via regularization method second continuous solution zero origin follows considering corresponding radial ode sub sup solutions method

Wen-shu Zhou  1   ; Xiao-dan Wei  1

1 Department of Mathematics Dalian Nationalities University 116600 Dalian, P.R. China 
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Wen-shu Zhou; Xiao-dan Wei. Multiplicity of solutions for a singular
 $p$-laplacian elliptic equation. Annales Polonici Mathematici, Tome 99 (2010) no. 2, pp. 157-180. doi: 10.4064/ap99-2-4

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