Geodesic
Positive solutions of superlinear elliptic~problems with discontinuous non-linearities
Izvestiya. Mathematics , Tome 85 (2021) no. 2, pp. 262-278

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We consider an elliptic boundary-value problem with a homogeneous Dirichlet boundary condition, a parameter and a discontinuous non-linearity. The positive parameter appears as a multiplicative term in the non-linearity, and the problem has a zero solution for any value of the parameter. The non-linearity has superlinear growth at infinity. We prove the existence of positive solutions by a topological method.
Keywords: superlinear elliptic problem, parameter, discontinuous non-linearity, topological method.
Mots-clés : positive solution 
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     author = {V. N. Pavlenko and D. K. Potapov},
     title = {Positive solutions of superlinear elliptic~problems with discontinuous non-linearities},
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V. N. Pavlenko; D. K. Potapov. Positive solutions of superlinear elliptic~problems with discontinuous non-linearities. Izvestiya. Mathematics , Tome 85 (2021) no. 2, pp. 262-278. http://geodesic.mathdoc.fr/item/IM2_2021_85_2_a3/