ON THE CONNECTION BETWEEN TWO QUASILINEAR ELLIPTIC PROBLEMS WITH SOURCE TERMS OF ORDER 0 OR 1

HAYDAR ABDEL HAMID, MARIE FRANÇOISE BIDAUT-VERON
2010 Communications in Contemporary Mathematics  
We establish a precise connection between two elliptic quasilinear problems with Dirichlet data in a bounded domain of R N : The ...rst one, of the form involves a source gradient term with natural growth, where is nonnegative, > 0; f (x) = 0, and is a nonnegative measure. The second one, of the form presents a source term of order 0; where g is nondecreasing, and is a nonnegative measure. Here and g can present an asymptote. The correlation gives new results of existence, nonexistence,
more » ... ty and multiplicity of the solutions for the two problems, without or with measures. New informations on the extremal solutions are given when g is superlinear.
doi:10.1142/s0219199710003993 fatcat:4dqst3yijzfavlrnphglytsi2e