Nonradial solutions of nonlinear Neumann problems in radially symmetric domains
Wang, Zhi-Qiang
Banach Center Publications, Tome 37 (1996), p. 85-96 / Harvested from The Polish Digital Mathematics Library
Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:251306
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     author = {Wang, Zhi-Qiang},
     title = {Nonradial solutions of nonlinear Neumann problems in radially symmetric domains},
     journal = {Banach Center Publications},
     volume = {37},
     year = {1996},
     pages = {85-96},
     zbl = {0864.35042},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv35i1p85bwm}
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Wang, Zhi-Qiang. Nonradial solutions of nonlinear Neumann problems in radially symmetric domains. Banach Center Publications, Tome 37 (1996) pp. 85-96. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv35i1p85bwm/

[000] [AM] Adimurthi and G. Mancini, The Neumann problem for elliptic equations with critical non-linearity, A tribute in honor of G.Prodi, Scuola Norm. Sup. Pisa (1991), 9-25.

[001] [AY] Adimurthi and S.L. Yadava, Existence and nonexistence of positive radial solutions of Neumann problems with Critical Sobolev exponents, Arch. Rat. Mech. Anal. 115 (1991), 275-296. | Zbl 0839.35041

[002] [AMY] Adimurthi, G. Mancini and S.L. Yadava, The role of the mean curvature in semilinear Neumann problem involving critical exponent, preprint. | Zbl 0847.35047

[003] [APY] Adimurthi, F. Pacella and S.L. Yadava, Interaction between the geometry of the boundary and positive solutions of a semilinear Neumann problem with critical nonlinearity, J. Func. Anal. 113 (1993), 318-350. | Zbl 0793.35033

[004] [BL] H. Brezis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proc. Am. Math. Soc. 88 (1983), 486-490. | Zbl 0526.46037

[005] [BN] H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical exponents, Comm. Pure Appl. Math. 36 (1983), 437-477. | Zbl 0541.35029

[006] [BKP] C. Budd, M.C. Knapp and L.A. Peletier, Asymptotic behavior of solutions of elliptic equations with critical exponents and Neumann boundary conditions, Proc. Roy. Soc. Edinburgh 117A (1991), 225-250. | Zbl 0733.35038

[007] [CL] C.-C. Chen and C.-S. Lin, Uniqueness of the ground state solution of -Δu + f(u) = 0, Comm. in PDEs 16 (1991), 1549-1572. | Zbl 0753.35034

[008] [GNN] B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations in Rn, Advances in Math., Supplementary Studies 7A (1981), 369-402.

[009] [KS] E.F. Keller and L.A. Segel, Initiation of slime mold aggregation viewed as an instability, J.Theor. Biol. 26 (1970), 399-415. | Zbl 1170.92306

[010] [KZ] M.K. Kwong and L. Zhang, Uniqueness of positive solutions of -Δu + f(u) = 0 in an annulus, Diff. Int. Equations 4 (1991), 583-599. | Zbl 0724.34023

[011] [L] P.L. Lions, The concentration-compactness principle in the calculus of variations, The locally compact case, Part 1 and Part 2, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), 109-145, 223-283. | Zbl 0541.49009

[012] [LN] C.-S. Lin and W.-M. Ni, On the diffusion coefficient of a semilinear Neumann problem, Lecture Notes in Math. 1340 (1988), 160-174, Springer-Verlag.

[013] [MW] J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer-Verlag, New York, 1989. | Zbl 0676.58017

[014] [MSW] S. Maier, K. Schmitt and Z.-Q. Wang, in preparation.

[015] [N] W.-M. Ni, On the positive radial solutions of some semilinear elliptic equations on RN, Appl. Math. Optim. 9 (1983), 373-380. | Zbl 0527.35026

[016] [NPT] W.-M. Ni, X.-B. Pan and I. Takagi, Singular behavior of least energy solutions of a semilinear Neumann problem involving critical Sobolev exponents, Duke Math. J. 67 (1992), 1-20.

[017] [NT1] W.-M. Ni and I. Takagi, On the shape of least-energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math. 45 (1991), 819-851. | Zbl 0754.35042

[018] [NT2] W.-M. Ni and I. Takagi, On the existence and shape of solutions to a semilinear Neumann problem, Progress in Nonlinear Diff. Equa. (Ed. Lloyd, Ni, Peletier and Serrin) (1992), 425-436. | Zbl 0792.35057

[019] [P] R. Palais, The principle of symmetric criticality, Comm. Math. Phys. 69 (1979), 19-30. | Zbl 0417.58007

[020] [Wx] X.-J. Wang, Neumann problems of semilinear elliptic equations involving critical Sobolev exponents, J. Diff. Equ. 93 (1991), 283-310. | Zbl 0766.35017

[021] [Wz1] Z.-Q. Wang, On the existence of multiple, single-peaked solutions of a semilinear Neumann problem, Arch. Rat. Mech. Anal. 120 (1992), 375-399. | Zbl 0784.35035

[022] [Wz2] Z.-Q. Wang, The effect of the domain geometry on the number of positive solutions of Neumann problems with critical exponents, Diff. and Integral Equations 8 (1995), 1533-1554. | Zbl 0829.35041

[023] [Wz3] Z.-Q. Wang, On the shape of solutions for a nonlinear Neumann problem in symmetric domains, Lectures in Applied Math. 29 (1993), 433-442. | Zbl 0797.35012

[024] [Wz4] Z.-Q. Wang, High energy and multi-peaked solutions for a nonlinear Neumann problem with critical exponent, Proc. Roy. Soc. Edinburgh 125A (1995), 1003-1029. | Zbl 0877.35050

[025] [Wz5] Z.-Q. Wang, On the existence and qualitative properties of solutions for a nonlinear Neumann problem with critical exponent, to appear in the Proceedings of World Congress of Nonlinear Analysts.

[026] [Wz6] Z.-Q. Wang, Construction of multi-peaked solutions for a nonlinear Neumann problem with critical exponent in symmetric domains, to appear in Nonlinear Anal. | Zbl 0862.35040