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Pavel Dr´abek, Zakaria Moudan, Abdelfettah Touzani EA=H DCAAKI AECAL=KA FH>A E R

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Pavel Dr´ abek, Zakaria Moudan, Abdelfettah Touzani

Nonlinear homogeneous eigenvalue problem in

RN

: nonstan- dard variational approach

Comment.Math.Univ.Carolinae 38,3 (1997) 421-431.

Abstract: The nonlinear eigenvalue problem for p-Laplacian

{ −div(a(x)|∇u|p−2∇u) =λg(x)|u|p−2uin RN, u >0 inRN,lim|x|→∞u(x) = 0, is considered. We assume that 1< p < N and that gis indefinite weight function.

The existence andC1,α-regularity of the weak solution is proved.

Keywords: eigenvalue, the p-Laplacian, indefinite weight, regularity AMS Subject Classification: Primary 35P30, 35J70

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