MULTIPLE NONTRIVIAL SOLUTIONS FOR A CLASS OF SEMILINEAR POLYHARMONIC EQUATIONS
In this paper, we are concerned with the following problem：{（-△）ku=λf（x）｜u｜q-2u＋g（x）｜u｜k＊-2u, x∈Ω, u∈H k0 （Ω）, where Ωis a bounded domain in RN with N ≥2k＋1, 1〈q〈2,λ〉0, f, g are continuous functions on Ω which are somewhere positive but which may change sign on Ω. k＊ = N2/N-2k is the critical Sobole...
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| Veröffentlicht in: | Acta mathematica scientia 2014-09, Vol.34 (5), p.1495-1509 |
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| container_title | Acta mathematica scientia |
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| creator | 尚月赟 王莉 |
| description | In this paper, we are concerned with the following problem：{（-△）ku=λf（x）｜u｜q-2u＋g（x）｜u｜k＊-2u, x∈Ω, u∈H k0 （Ω）, where Ωis a bounded domain in RN with N ≥2k＋1, 1〈q〈2,λ〉0, f, g are continuous functions on Ω which are somewhere positive but which may change sign on Ω. k＊ = N2/N-2k is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple nontrivial solutions to this equation is verified. |
| doi_str_mv | 10.1016/S0252-9602(14)60099-0 |
| format | Article |
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| fulltext | fulltext |
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| ispartof | Acta mathematica scientia, 2014-09, Vol.34 (5), p.1495-1509 |
| issn | 0252-9602 1572-9087 |
| language | eng |
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| source | Access via ScienceDirect (Elsevier); Alma/SFX Local Collection |
| subjects | critical exponents Exponents Functions (mathematics) Manifolds Mathematical analysis nontrivial solutions polyharmonic problems variational methods 临界指数 半线性 多解 多重调和方程 连续函数 非平凡解 |
| title | MULTIPLE NONTRIVIAL SOLUTIONS FOR A CLASS OF SEMILINEAR POLYHARMONIC EQUATIONS |
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