This paper considers the following quasilinear elliptic problem [GRAPHICS] where Omega is a bounded regular domain in R-N (N greater than or equal to 3), N > p > 1. When g(u) satisfies suitable conditions and g(...This paper considers the following quasilinear elliptic problem [GRAPHICS] where Omega is a bounded regular domain in R-N (N greater than or equal to 3), N > p > 1. When g(u) satisfies suitable conditions and g(u)u - beta integral (u)(0) g(s)ds is unbounded, a(x) is a Holder continuous function which changes sign on Omega and integral (Omega-) \a(x)\ dx is suitably small. The authors prove the existence of a nonnegative nontrivial solution for N > p > 1. in particular, the existence of a positive solution to the problem for N > p greater than or equal to 2. Our main theorem generalizes a recent result of Samia Khanfir and Leila Lassoued (see [1]) concerning the case where p = 2. They prove also that if g(u) = \u \ (q-2)u with p < q < p* and Omega (+) = {x is an element ofQ \a(x) > 0} is a nonempty open set, then the above problem possesses infinitely many solutions.展开更多
文摘This paper considers the following quasilinear elliptic problem [GRAPHICS] where Omega is a bounded regular domain in R-N (N greater than or equal to 3), N > p > 1. When g(u) satisfies suitable conditions and g(u)u - beta integral (u)(0) g(s)ds is unbounded, a(x) is a Holder continuous function which changes sign on Omega and integral (Omega-) \a(x)\ dx is suitably small. The authors prove the existence of a nonnegative nontrivial solution for N > p > 1. in particular, the existence of a positive solution to the problem for N > p greater than or equal to 2. Our main theorem generalizes a recent result of Samia Khanfir and Leila Lassoued (see [1]) concerning the case where p = 2. They prove also that if g(u) = \u \ (q-2)u with p < q < p* and Omega (+) = {x is an element ofQ \a(x) > 0} is a nonempty open set, then the above problem possesses infinitely many solutions.
