A note on discontinuous problem with a free boundary | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 19, Issue 1, June 2011, Pages 86-87 PDF (309.08 K) | ||
| DOI: 10.1016/j.joems.2011.09.002 | ||
| Authors | ||
| Sabri Bensid* ; Sidi Mohammed Bouguima | ||
| Department of Mathematics, Faculty of Science, University of Tlemcen, B.P. 119, Tlemcen 13000, Algeria | ||
| Abstract | ||
| We study a nonlinear elliptic problem with discontinuous nonlinearity ðPÞ Du ¼ fðuÞHðl uÞ in X; u ¼0 on @X; where H is the Heaviside’s unit function, f, h are given functions and l is a positive real parameter. We prove the existence of a unique solution and characterize the corresponding free boundary. Our methods relies on variational inequality approach combining with fixed point arguments. | ||
| Keywords | ||
| Variational inequalities; Uniqueness; Free boundary | ||
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