The existence and multiplicity of positive solutions are studied for a class of quasi- linear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational...The existence and multiplicity of positive solutions are studied for a class of quasi- linear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques.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
This paper investigates sub-linear elliptic equations on self-similar fractal sets. With an appropriately defined Laplacian, we obtain the existence of nontrivial solutions of sub-linear elliptic equations -△u=λu- a...This paper investigates sub-linear elliptic equations on self-similar fractal sets. With an appropriately defined Laplacian, we obtain the existence of nontrivial solutions of sub-linear elliptic equations -△u=λu- a（x）｜u｜q-1u-f（x,u）,with zero boundary Dirichlet conditions. The results are obtained by using Mountain Pass Lemma and Saddle Point Theorem.展开更多
基金Supported by National Natural Science Foundation of China (11071198 11101347)+2 种基金Postdoctor Foundation of China (2012M510363)the Key Project in Science and Technology Research Plan of the Education Department of Hubei Province (D20112605 D20122501)
文摘The existence and multiplicity of positive solutions are studied for a class of quasi- linear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques.
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.
文摘This paper investigates sub-linear elliptic equations on self-similar fractal sets. With an appropriately defined Laplacian, we obtain the existence of nontrivial solutions of sub-linear elliptic equations -△u=λu- a（x）｜u｜q-1u-f（x,u）,with zero boundary Dirichlet conditions. The results are obtained by using Mountain Pass Lemma and Saddle Point Theorem.
