This paper deals with superlinear fourth-order elliptic problem under Navier boundary condition. By using the mountain pass theorem and suitable truncation, a multiplicity result is established for all λ〉 0 and some...This paper deals with superlinear fourth-order elliptic problem under Navier boundary condition. By using the mountain pass theorem and suitable truncation, a multiplicity result is established for all λ〉 0 and some previous result is extended.展开更多
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
基金The 985 Program of Jilin Universitythe Science Research Foundation for Excellent Young Teachers of College of Mathematics at Jilin University
文摘This paper deals with superlinear fourth-order elliptic problem under Navier boundary condition. By using the mountain pass theorem and suitable truncation, a multiplicity result is established for all λ〉 0 and some previous result is extended.
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.
