Infinitely many solutions for p‐Kirchhoff equation with concave–convex nonlinearities in |
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Authors: | Caisheng Chen Qiang Chen |
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Institution: | 1. College of Science, Hohai University, Nanjing, China;2. Yancheng Institute of Technology, Yancheng, China |
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Abstract: | In this paper, we study the existence of infinitely many solutions to p‐Kirchhoff‐type equation (0.1) where f(x,u) = λh1(x)|u|m ? 2u + h2(x)|u|q ? 2u,a≥0,μ > 0,τ > 0,λ≥0 and . The potential function verifies , and h1(x),h2(x) satisfy suitable conditions. Using variational methods and some special techniques, we prove that there exists λ0>0 such that problem 0.1 admits infinitely many nonnegative high‐energy solutions provided that λ∈0,λ0) and . Also, we prove that problem 0.1 has at least a nontrivial solution under the assumption f(x,u) = h2|u|q ? 2u,p < q< min{p*,p(τ + 1)} and has infinitely many nonnegative solutions for f(x,u) = h1|u|m ? 2u,1 < m < p. Copyright © 2015 John Wiley & Sons, Ltd. |
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Keywords: | p‐Kirchhoff equation symmetric mountain pass lemma variational methods |
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