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.
Bensid, S., & Bouguima, S. M. (2011). A note on discontinuous problem with a free boundary. Journal of the Egyptian Mathematical Society, 19(1), 86-87. doi: 10.1016/j.joems.2011.09.002
MLA
Sabri Bensid; Sidi Mohammed Bouguima. "A note on discontinuous problem with a free boundary", Journal of the Egyptian Mathematical Society, 19, 1, 2011, 86-87. doi: 10.1016/j.joems.2011.09.002
HARVARD
Bensid, S., Bouguima, S. M. (2011). 'A note on discontinuous problem with a free boundary', Journal of the Egyptian Mathematical Society, 19(1), pp. 86-87. doi: 10.1016/j.joems.2011.09.002
VANCOUVER
Bensid, S., Bouguima, S. M. A note on discontinuous problem with a free boundary. Journal of the Egyptian Mathematical Society, 2011; 19(1): 86-87. doi: 10.1016/j.joems.2011.09.002
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