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Existence of nontrivial solutions for p-Laplacian-Like equations

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Abstract

In this paper, we study the p-Laplacian-Like equations involving Hardy potential or involving critical exponent and prove the existence of one or infinitely many nontrivial solutions. The results of the equations discussed can be applied to a variety of different fields in applied mechanics.

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References

  1. Chen Z.C., Luo T. The eigenvalue problem for p-Laplacian-Like equations. Acta Math. Sinica, 46(4): 631–638 (2003) (in Chinese)

    MathSciNet  MATH  Google Scholar 

  2. Shen Y.T., Li Z.X. The eigenvalue problem for p-Laplacian equation with critical exponent. J. South China Univ. of Tech., 33(11): 111–114 (2005) (in Chinese)

    Google Scholar 

  3. Shen Y.T., Yan S.S. Variational methods in nonlinear elliptic equations. South China Univ. of Tech. Press, Second Edition, Guangzhou, 1999 (in Chinese)

    Google Scholar 

  4. Pellacci B. Multiple critical points for nondifferentiable functionals involving Hardy potentials. Nonlinear Anal., 61: 517–542 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Lions P.L. The concentration-compactness principle in the calculus of varations, The locally compact case, part I and part II. Rev. Mat. Iberoamericana, 1: 145–201, 223–283 (1985)

    MathSciNet  MATH  Google Scholar 

  6. Lions P.L. The concentration-compactness principle in the calculus of varations, The limit case, part I and part II. Ann. Inst. H. Poincare Anal. Non Lineaire, 1: 109–145, 45–121 (1984)

    MathSciNet  MATH  Google Scholar 

  7. Rabinowitz P.H. Multiple critical points of perturbed symmetric functionals. Trans. Amer. Math. Soc., 272(2): 753–769 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  8. Rabinowitz P.H. Minimax methods in critical point theory with applications to differential equations. CBMS Regional Conf. Ser. in Math., No.65, Amer. Math. Soc., Providence, R. I., 1986

    Google Scholar 

  9. Clark David C. A variant of the Lusternik-Schnirelman theory. J. Indiana Univ. Math., 22(1): 65–74 (1972)

    Article  MATH  Google Scholar 

  10. Ghoussoub N., Yuan C. Multiple solutions for quasilinear PDES involving the critical Sobolev and Hardy exponents. Trans. Amer. Math. Soc., 352(12): 5703–5743 (2000)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, South China University of Technology, Guangzhou, 510640, China

    Zhou-xin Li & Yao-tian Shen

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  1. Zhou-xin Li
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  2. Yao-tian Shen
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Correspondence to Zhou-xin Li.

Additional information

Supported by the National Natural Science Foundation of China (No. 10771074).

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Li, Zx., Shen, Yt. Existence of nontrivial solutions for p-Laplacian-Like equations. Acta Math. Appl. Sin. Engl. Ser. 27, 393–406 (2011). https://doi.org/10.1007/s10255-011-0079-5

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  • DOI: https://doi.org/10.1007/s10255-011-0079-5

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