Nontrivial solutions of elliptic equations with supercritical exponent in contractible domains

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Nontrivial solutions of elliptic equations with supercritical exponent in contractible domains

Donato Passaseo

Source: Duke Math. J. Volume 92, Number 2 (1998), 429-457.

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Primary Subjects: 35J65

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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077231492
Mathematical Reviews number (MathSciNet): MR1612734
Zentralblatt MATH identifier: 0943.35034
Digital Object Identifier: doi:10.1215/S0012-7094-98-09213-4

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References

[1] Adimurthi and S. L. Yadava, Elementary proof of the nonexistence of nodal solutions for the semilinear elliptic equations with critical Sobolev exponent, Nonlinear Anal. 14 (1990), no. 9, 785–787.

Mathematical Reviews (MathSciNet): MR92j:35056

Zentralblatt MATH: 0706.35048

[2] A. Ambrosetti and M. Struwe, A note on the problem $-\Delta u=\lambda u+u\vert u\vert \sp 2\sp \ast-2$, Manuscripta Math. 54 (1986), no. 4, 373–379.

Mathematical Reviews (MathSciNet): MR87h:35076

Zentralblatt MATH: 0596.35043

Digital Object Identifier: doi:10.1007/BF01168482

[3] F. V. Atkinson, H. Brezis, and L. A. Peletier, Solutions d'équations elliptiques avec exposant de Sobolev critique qui changent de signe, C. R. Acad. Sci. Paris Sér. I Math. 306 (1988), no. 16, 711–714.

Mathematical Reviews (MathSciNet): MR89k:35088

Zentralblatt MATH: 0696.35059

[4] A. Bahri and J. M. Coron, On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain, Comm. Pure Appl. Math. 41 (1988), no. 3, 253–294.

Mathematical Reviews (MathSciNet): MR89c:35053

Zentralblatt MATH: 0649.35033

Digital Object Identifier: doi:10.1002/cpa.3160410302

[5] H. Brezis, Elliptic equations with limiting Sobolev exponents—the impact of topology, Comm. Pure Appl. Math. 39 (1986), no. S, suppl., S17–S39.

Mathematical Reviews (MathSciNet): MR87k:58272

Zentralblatt MATH: 0601.35043

Digital Object Identifier: doi:10.1002/cpa.3160390704

[6] H. Brézis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), no. 4, 437–477.

Mathematical Reviews (MathSciNet): MR84h:35059

Zentralblatt MATH: 0541.35029

Digital Object Identifier: doi:10.1002/cpa.3160360405

[7] H. Brezis and L. Nirenberg, A minimization problem with critical exponent and nonzero data, Ann. Scuola Norm. Sup. Pisa Cl. Sci (4) 16 (1989), 129–140.

Zentralblatt MATH: 0763.46023

[8] A. Capozzi, D. Fortunato, and G. Palmieri, An existence result for nonlinear elliptic problems involving critical Sobolev exponent, Ann. Inst. H. Poincaré Anal. Non Linéaire 2 (1985), no. 6, 463–470.

Mathematical Reviews (MathSciNet): MR87j:35126

Zentralblatt MATH: 0612.35053

[9] G. Cerami, D. Fortunato, and M. Struwe, Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), no. 5, 341–350.

Mathematical Reviews (MathSciNet): MR86e:35016

Zentralblatt MATH: 0568.35039

[10] G. Cerami, S. Solimini, and M. Struwe, Some existence results for superlinear elliptic boundary value problems involving critical exponents, J. Funct. Anal. 69 (1986), no. 3, 289–306.

Mathematical Reviews (MathSciNet): MR88b:35074

Zentralblatt MATH: 0614.35035

Digital Object Identifier: doi:10.1016/0022-1236(86)90094-7

[11] E. N. Dancer, A note on an equation with critical exponent, Bull. London Math. Soc. 20 (1988), no. 6, 600–602.

Mathematical Reviews (MathSciNet): MR90e:35011

Zentralblatt MATH: 0646.35027

Digital Object Identifier: doi:10.1112/blms/20.6.600

[12] W. Ding, Positive solutions of $\Delta u+u\sp (n+2)/(n-2)=0$ on contractible domains, J. Partial Differential Equations 2 (1989), no. 4, 83–88.

Mathematical Reviews (MathSciNet): MR91a:35012

Zentralblatt MATH: 0694.35067

[13] F. Merle and L. A. Peletier, Asymptotic behaviour of positive solutions of elliptic equations with critical and supercritical growth. I. The radial case, Arch. Rational Mech. Anal. 112 (1990), no. 1, 1–19.

Mathematical Reviews (MathSciNet): MR91m:35046

Zentralblatt MATH: 0719.35004

Digital Object Identifier: doi:10.1007/BF00431720

[14] F. Merle and L. A. Peletier, Asymptotic behaviour of positive solutions of elliptic equations with critical and supercritical growth. II. The nonradial case, J. Funct. Anal. 105 (1992), no. 1, 1–41.

Mathematical Reviews (MathSciNet): MR93e:35039

Zentralblatt MATH: 0771.35008

Digital Object Identifier: doi:10.1016/0022-1236(92)90070-Y

[15] F. Merle and L. A. Peletier, Positive solutions of elliptic equations involving supercritical growth, Proc. Roy. Soc. Edinburgh Sect. A 118 (1991), no. 1-2, 49–62.

Mathematical Reviews (MathSciNet): MR92g:35074

Zentralblatt MATH: 0742.35025

[16] C. Miranda, Un'osservazione su un teorema di Brouwer, Boll. Un. Mat. Ital. (2) 3 (1940), 5–7.

Mathematical Reviews (MathSciNet): MR3,60b

Zentralblatt MATH: 0024.02203

[17] D. Passaseo, Multiplicity of positive solutions of nonlinear elliptic equations with critical Sobolev exponent in some contractible domains, Manuscripta Math. 65 (1989), no. 2, 147–165.

Mathematical Reviews (MathSciNet): MR90g:35051

Zentralblatt MATH: 0701.35068

Digital Object Identifier: doi:10.1007/BF01168296

[18] D. Passaseo, On some sequences of positive solutions of elliptic problems with critical Sobolev exponent, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 3 (1992), no. 1, 15–21.

Mathematical Reviews (MathSciNet): MR93c:35049

Zentralblatt MATH: 0778.35036

[19] D. Passaseo, Existence and multiplicity of positive solutions for elliptic equations with supercritical nonlinearity in contractible domains, Rend. Accad. Naz. Sci. XL Mem. Mat. (5) 16 (1992), 77–98.

Mathematical Reviews (MathSciNet): MR94b:35024

Zentralblatt MATH: 0831.35064

[20] D. Passaseo, Multiplicity of positive solutions for the equation $\Delta u+\lambda u+u\sp 2\sp *-1=0$ in noncontractible domains, Topol. Methods Nonlinear Anal. 2 (1993), no. 2, 343–366.

Mathematical Reviews (MathSciNet): MR94k:35099

Zentralblatt MATH: 0810.35029

[21] D. Passaseo, Nonexistence results for elliptic problems with supercritical nonlinearity in nontrivial domains, J. Funct. Anal. 114 (1993), no. 1, 97–105.

Mathematical Reviews (MathSciNet): MR94m:35118

Zentralblatt MATH: 0793.35039

Digital Object Identifier: doi:10.1006/jfan.1993.1064

[22] D. Passaseo, The effect of the domain shape on the existence of positive solutions of the equation $\Delta u+u\sp 2\sp *-1=0$, Topol. Methods Nonlinear Anal. 3 (1994), no. 1, 27–54.

Mathematical Reviews (MathSciNet): MR95d:35014

Zentralblatt MATH: 0812.35032

[23] D. Passaseo, New nonexistence results for elliptic equations with supercritical nonlinearity, Differential Integral Equations 8 (1995), no. 3, 577–586.

Mathematical Reviews (MathSciNet): MR95j:35086

Zentralblatt MATH: 0821.35056

[24] D. Passaseo, Some sufficient conditions for the existence of positive solutions to the equation $-\Delta u+a(x)u=u\sp 2\sp *-1$ in bounded domains, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996), no. 2, 185–227.

Mathematical Reviews (MathSciNet): MR97i:35055

Zentralblatt MATH: 0848.35046

[25] D. Passaseo, Multiplicity of nodal solutions for elliptic equations with supercritical exponent in contractible domains, to appear in Topol. Methods Nonlinear Anal.

Mathematical Reviews (MathSciNet): MR1483626

Zentralblatt MATH: 0901.35034

[26] D. Passaseo, Multiple solutions of elliptic problems with supercritical growth in contractible domains, in preparation.

[27] S. I. Pohozaev, Eigenfunctions of the equation $\Delta u+\lambda f(u)=0$, Sov. Math. Dokl. 6 (1965), 1408–1411.

Zentralblatt MATH: 0141.30202

Mathematical Reviews (MathSciNet): MR192184

[28] O. Rey, Sur un problème variationnel non compact: l'effet de petits trous dans le domaine, C. R. Acad. Sci. Paris Sér. I Math. 308 (1989), no. 12, 349–352.

Mathematical Reviews (MathSciNet): MR90h:35101

Zentralblatt MATH: 0686.35047

[29] O. Rey, A multiplicity result for a variational problem with lack of compactness, Nonlinear Anal. 13 (1989), no. 10, 1241–1249.

Mathematical Reviews (MathSciNet): MR91a:35076

Zentralblatt MATH: 0702.35101

[30] S. Solimini, On the existence of infinitely many radial solutions for some elliptic problems, to appear in Rev. Mat. Apl.

Mathematical Reviews (MathSciNet): MR926233

Zentralblatt MATH: 0663.35023

[31] G. Tarantello, Nodal solutions of semilinear elliptic equations with critical exponent, to appear in Differential Integral Equations.

Mathematical Reviews (MathSciNet): MR1141725

[32] D. Zhang, On multiple solutions of $\Delta u+\lambda u+\vert u\vert \sp 4/(n-2)u=0$, Nonlinear Anal. 13 (1989), no. 4, 353–372.

Mathematical Reviews (MathSciNet): MR90i:35111

Zentralblatt MATH: 0704.35053

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