Multiplicity results for semilinear elliptic equations in a bounded domain of 2 involving critical exponents
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 17 (1990) no. 4, p. 481-504
@article{ASNSP_1990_4_17_4_481_0,
     author = {Adimurthi and Yadava, S. L.},
     title = {Multiplicity results for semilinear elliptic equations in a bounded domain of $\mathbb {R}^2$ involving critical exponents},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 17},
     number = {4},
     year = {1990},
     pages = {481-504},
     zbl = {0732.35029},
     mrnumber = {1093706},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1990_4_17_4_481_0}
}
Adimurthi; Yadava, S. L. Multiplicity results for semilinear elliptic equations in a bounded domain of $\mathbb {R}^2$ involving critical exponents. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 17 (1990) no. 4, pp. 481-504. http://www.numdam.org/item/ASNSP_1990_4_17_4_481_0/

[1] Adimurthi, Existence of positive solutions of the semilinear Dirichlet problem with critical growth for the n-Laplacian, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 17, 1990, pp. 393-413. | Numdam | Zbl 0732.35028

[2] Adimurthi - S.L. Yadava, Elementary proof of the non-existence of nodal solutions for the semilinear elliptic equations with critical Sobolev exponent, Nonlinear Analysis TMA 14, 1990. | Zbl 0706.35048

[3] Adimurthi - S.L. Yadava, Bifurcation results for semilinear elliptic problem with critical exponent in R2, Nonlinear Analysis TMA 14, (1990), pp. 607-612. | Zbl 0702.35015

[4] Adimurthi, S.L. Yadava, A note on non-existence of nodal solutions of the semilinear elliptic equations with critical exponent in R2, Trans. Amer. Math. Soc., to appear.

[5] A. Ambrosetti - P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), pp. 349-381. ' | Zbl 0273.49063

[6] F.V. Atkinson - H. Brezis - L.A. Peletier, Nodal solutions of elliptic equations with critical Sobolev exponents, C.R. Acad. Sci. Paris t-306 Série 1 (1988), pp. 711-714. | Zbl 0696.35059

[7] P. Bartolo - V. Benci - D. Fortunato, Abstract critical point Theorem and applications to some nonlinear problems with "strong resonance" at infinity. Nonlinear Analysis TMA 7 (1983), pp. 981-1012. | Zbl 0522.58012

[8] H. Brezis - L. Nirenberg, Positive solutions of non-linear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), pp. 437-477. | Zbl 0541.35029

[9] A. Capozzi - D. Fortunato - G. Palmieri, An existence result for nonlinear elliptic problems involving critical Sobolev exponent, Ann. Inst. Henri Poincaré 2 (1985), pp. 463-470. | Numdam | Zbl 0612.35053

[10] G. Cerami - S. Solimini - M. Struwe, Some existence results for superlinear elliptic boundary value problems involving critical exponents, J. Funct. Anal. 69 (1986), pp. 289-306. | Zbl 0614.35035

[11] D. Fortunato - E. Jannelli, Infinitely many solutions for some nonlinear elliptic problems in symmetrical domains, Proc. Roy. Soc. Edinburgh 105 (1987), pp. 205-213. | Zbl 0676.35024

[12] C. Miranda, Un'osservazione sul teorema di Brouwer, Boll. Un. Mat. Ital. Ser. II Anno III 19 (1940), pp. 5-7. | JFM 66.0217.01 | Zbl 0024.02203

[13] Z. Nehari, Characteristic values associated with a class of nonlinear second-order differential equations, Acta Mathematica 105 (1961), pp. 141-175. | Zbl 0099.29104

[14] S. Solimini, On the existence of inifinitely many radial solutions for some elliptic problems, Preprint.