Multiple solutions for a class of Kirchhoff type problems with concave nonlinearity |
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Authors: | Bitao Cheng Xian Wu Jun Liu |
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Affiliation: | 1. Department of Mathematics and Information Science, Qujing Normal University, Qujing, 655011, Yunnan, People’s Republic of China 2. Department of Mathematics, Yunnan Normal University, Kunming, 650092, Yunnan, People’s Republic of China
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Abstract: | In the present paper, by applying variant mountain pass theorem and Ekeland variational principle we study the existence of multiple nontrivial solutions for a class of Kirchhoff type problems with concave nonlinearity $$ left{begin{array}{ll} -(a + b intnolimits_{Omega} |nabla{u}|^{2})triangle{u} = alpha(x)|u|^{q-2}u + f(x, u),quad{rm in};Omega, u = 0,;quadqquadquadqquadqquadqquadqquadqquadqquadqquad{rm on};partialOmega, end{array} right. $$ A new existence theorem and an interesting corollary of four nontrivial solutions are obtained. |
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