A note on discontinuous problem with a free boundary | ||||
| Journal of the Egyptian Mathematical Society | ||||
| Volume 19, Issue 1, June 2011, Page 86-87 PDF (309.08 K) | ||||
| DOI: 10.1016/j.joems.2011.09.002 | ||||
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| Authors | ||||
Sabri Bensid  ; Sidi Mohammed Bouguima
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| 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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