Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We consider the linear eigenvalue problem -Δu = λV(x)u, $u ∈ D^{1,2}_0(Ω)$, and its nonlinear generalization $-Δ_{p}u = λV(x)|u|^{p-2}u$, $u ∈ D^{1,p}_0(Ω)$. The set Ω need not be bounded, in particular, $Ω = ℝ^N$ is admitted. The weight function V may change sign and may have singular points. We show that there exists a sequence of eigenvalues $λ_n → ∞$.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
191-201
Opis fizyczny
Daty
wydano
1999
poprawiono
1998-11-26
otrzymano
1999-06-04
Twórcy
autor
- Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden, andrzejs@matematik.su.se
autor
- Institut de Mathématique Pure et Appliquée, Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium, Willem@amm.ucl.ac.be
Bibliografia
- [1] W. Allegretto, Principal eigenvalues for indefinite-weight elliptic problems in $R^n$, Proc. Amer. Math. Soc. 116 (1992), 701-706.
- [2] W. Allegretto and Y. X. Huang, Eigenvalues of the indefinite-weight p-Laplacian in weighted spaces, Funkc. Ekvac. 38 (1995), 233-242.
- [3] K. J. Brown, C. Cosner and J. Fleckinger, Principal eigenvalues for problems with indefinite weight function on $R^N$, Proc. Amer. Math. Soc. 109 (1990), 147-155.
- [4] K. J. Brown and A. Tertikas, The existence of principal eigenvalues for problems with indefinite weight function on $ℝ^k$, Proc. Roy. Soc. Edinburgh Sect. A 123 (1993), 561-569.
- [5] J.-N. Corvellec, M. Degiovanni and M. Marzocchi, Deformation properties for continuous functionals and critical point theory, Topol. Methods Nonlinear Anal. 1 (1993), 151-171.
- [6] P. Drábek and Y. X. Huang, Bifurcation problems for the p-Laplacian in $R^N$, Trans. Amer. Math. Soc. 349 (1997), 171-188.
- [7] P. Drábek, Z. Moudan and A. Touzani, Nonlinear homogeneous eigenvalue problem in $R^N$: nonstandard variational approach, Comm. Math. Univ. Carolin. 38 (1997), 421-431.
- [8] J. Fleckinger, R. F. Manásevich, N. M. Stavrakakis and F. de Thélin, Principal eigenvalues for some quasilinear elliptic equations on $ℝ^N$, Adv. Differential Equations 2 (1997), 981-1003.
- [9] J. P. Garcia Azorero and I. Peral Alonso, Hardy inequalities and some critical elliptic and parabolic problems, J. Differential Equations 144 (1998), 441-476.
- [10] Y. X. Huang, Eigenvalues of the p-Laplacian in $R^N$ with indefinite weight, Comm. Math. Univ. Carolin. 36 (1995), 519-527.
- [11] D. Jerison and C. E. Kenig, Unique continuation and absence of positive eigenvalues for Schrödinger operators, Ann. of Math. 121 (1985), 463-494.
- [12] E. H. Lieb and M. Loss, Analysis, Amer. Math. Soc., Providence, R.I., 1997.
- [13] V. G. Maz'ja, Sobolev Spaces, Springer, Berlin, 1985.
- [14] P. H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conf. Ser. in Math. 65, Amer. Math. Soc., Providence, R.I., 1986.
- [15] G. Rozenblum and M. Solomyak, On principal eigenvalues for indefinite problems in Euclidean space, Math. Nachr. 192 (1998), 205-223.
- [16] M. Struwe, Variational Methods, Springer, Berlin, 1990.
- [17] A. Szulkin, Ljusternik-Schnirelmann theory on $C^1$-manifolds, Ann. Inst. H. Poincaré Anal. Non Linéaire 5 (1988), 119-139.
- [18] A. Tertikas, Critical phenomena in linear elliptic problems, J. Funct. Anal. 154 (1998), 42-66.
- [19] M. Willem, Analyse Harmonique Réelle, Hermann, Paris, 1995.
- [20] M. Willem, Minimax Theorems, Birkhäuser, Boston, 1996.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv135i2p191bwm