Nonradial solutions of nonlinear Neumann problems in radially symmetric domains

• Autorzy: Zhi-Qiang Wang
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 35
• Numer: 1
• Strony: 85-96

Daty

wydano

1996

Twórcy

autor

Zhi-Qiang Wang

• Department of Mathematics and Statistics, Utah State University, Logan, Utah 84322, U.S.A.

Bibliografia

• [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.
• [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.
• [AMY] Adimurthi, G. Mancini and S.L. Yadava, The role of the mean curvature in semilinear Neumann problem involving critical exponent, preprint.
• [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.
• [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.
• [BN] H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical exponents, Comm. Pure Appl. Math. 36 (1983), 437-477.
• [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.
• [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.
• [GNN] B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations in $R^n$, Advances in Math., Supplementary Studies 7A (1981), 369-402.
• [KS] E.F. Keller and L.A. Segel, Initiation of slime mold aggregation viewed as an instability, J.Theor. Biol. 26 (1970), 399-415.
• [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.
• [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.
• [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.
• [MW] J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer-Verlag, New York, 1989.
• [MSW] S. Maier, K. Schmitt and Z.-Q. Wang, in preparation.
• [N] W.-M. Ni, On the positive radial solutions of some semilinear elliptic equations on $R^N$, Appl. Math. Optim. 9 (1983), 373-380.
• [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.
• [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.
• [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.
• [P] R. Palais, The principle of symmetric criticality, Comm. Math. Phys. 69 (1979), 19-30.
• [Wx] X.-J. Wang, Neumann problems of semilinear elliptic equations involving critical Sobolev exponents, J. Diff. Equ. 93 (1991), 283-310.
• [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.
• [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.
• [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.
• [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.
• [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.
• [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.