Autor

DOI:

https://doi.org/10.12775/TMNA.2020.080

Słowa kluczowe

Abstrakt

Bibliografia

D.R. Adams, A sharp inequality of J. Moser for higher order derivatives, Ann. of Math. (2) 128 (1988), no. 2, 385–398.

W. Allegretto and Y.X. Huang, A Picone’s identity for the p-Laplacian and applications, Nonlinear Anal. 32 (1998), no. 7, 819–830.

A. Ambrosetti and A. Malchiodi, Nonlinear Analysis and Semilinear Elliptic Problems, vol. 104, Cambridge University Press, Cambridge, 2007.

T.V. Anoop, On Weighted Eigenvalue Problems and Applications, The Institute of Mathematical Sciences, Chennai, 2011, pp. 1–159.

T.V. Anoop, A note on generalized Hardy–Sobolev inequalities, Int. J. Anal. (2013), Art. ID 784398, 9 pp.

T.V. Anoop, P. Drábek, L. Sankar and S. Sasi, Antimaximum principle in exterior domains, Nonlinear Anal. 130 (2016), 241–254.

T.V. Anoop, M. Lucia and M. Ramaswamy, Eigenvalue problems with weights in Lorentz spaces, Calc. Var. Partial Differential Equations 36 (2009), no. 3, 355–376.

D. Arcoya and J.L. Gámez, Bifurcation theory and related problems: anti-maximum principle and resonance, Comm. Partial Differential Equations 26 (2001), no. 9–10, 1879–1911.

L. Bauer, E.L. Reiss and H.B. Keller, Axisymmetric buckling of hollow spheres and hemispheres, Comm. Pure Appl. Math. 23 (1970), 529–568.

C. Bennett and K. Rudnick, On Lorentz–Zygmund spaces, Dissertationes Math. (Rozprawy Mat.), 175 (1980), 67 pp.

F.E. Browder, Nonlinear elliptic boundary value problems and the generalized topological degree, Bull. Amer. Math. Soc. 76 (1970), 999–1005.

K.J. Brown, Local and global bifurcation results for a semilinear boundary value problem, J. Differential Equations 239 (2007), no. 2, 296–310.

K.J. Brown and A. Tertikas, On the bifurcation of radially symmetric steady-state solutions arising in population genetics, SIAM J. Math. Anal. 22 (1991), no. 2, 400–413.

A. Cianchi, R. Kerman and L. Pick, Boundary trace inequalities and rearrangements, J. Anal. Math. 105 (2008), 241–265.

J.M. Cushing, Some existence theorems for nonlinear eigenvalue problems associated with elliptic equations, Arch. Rational Mech. Anal. 42 (1971), 63–76.

J.M. Cushing, Nonlinear Steklov problems on the unit circle II. And a hydrodynamical application, J. Math. Anal. Appl. 39 (1972), 267–278; errata, ibid. 41 (1973), 536–537.

E.N. Dancer, On the structure of solutions of non-linear eigenvalue problems, Indiana Univ. Math. J. 23 (1973/74), 1069–1076.

E.N. Dancer, Bifurcation from simple eigenvalues and eigenvalues of geometric multiplicity one, Bull. London Math. Soc. 34 (2002), no. 5, 533–538.

P. Drábek, On the global bifurcation for a class of degenerate equations, Ann. Mat. Pura Appl. (4) 159 (1991), 1–16.

P. Drábek and Y.X. Huang, Bifurcation problems for the p-Laplacian in RN , Trans. Amer. Math. Soc. 349 (1997), 171–188.

P. Drábek and J. Milota, Methods of Nonlinear Analysis, Birkhäuser Advanced Texts: Basler Lehrbücher, Birkhäuser–Verlag, Basel, 2013.

D.E. Edmunds and W.D. Evans, Hardy Operators, Function Spaces and Embeddings, Springer Monographs in Mathematics, Springer–Verlag, Berlin, 2004.

D.E. Edmunds and H. Triebel, Sharp Sobolev embeddings and related Hardy inequalities: the critical case, Math. Nachr. 207 (1999), 79–92.

V. Felli, E.M. Marchini and S. Terracini, On Schrödinger operators with multisingular inverse-square anisotropic potentials, Indiana Univ. Math. J. 58 (2009), no. 2, 617–676.

L.C.F. Ferreira and S.L.N. Neves, On elliptic equations with singular potentials and nonlinear boundary conditions, Quart. Appl. Math. 76 (2018), no. 4, 699–711.

W.M. Frank, D.J. Land and R.M. Spector, Singular potentials, Rev. Modern Phys. 43 (1971), no. 1, 36–98.

J. Giacomoni, M. Lucia and M. Ramaswamy, Some elliptic semilinear indefinite problems on RN , Proc. Roy. Soc. Edinburgh Sect. A 134 (2004), no. 2, 333–361.

P. Girg and P. Takáč, Bifurcations of positive and negative continua in quasilinear elliptic eigenvalue problems, Ann. Henri Poincaré 9 (2008), no. 2, 275–327.

R.A. Hunt, On L(p, q) spaces, Enseign. Math. (2) 12 (1966), 249–276.

J.B. Keller and S. Antman (eds.), Bifurcation Theory and Nonlinear Eigenvalue Problems, W.A. Benjamin, Inc., New York, Amsterdam, 1969.

M.A. Krasnosel’skiı̆, Topological Methods in the Theory of Nonlinear Integral Equations, The Macmillan Co., New York, 1964.

J. Leray and J. Schauder, Topologie et équations fonctionnelles, Ann. Sci. École Norm. Sup. (3) 51 (1934), 45–78.

C.T. Levi, Dtermination rigoureuse des ondes permanentes d’ampleur finie, Mathematische Annalen 93 (1925), 264–314.

E.H. Lieb and M. Loss, Analysis, Graduate Studies in Mathematics, vol. 14, American Mathematical Society, Providence, RI, 2001.

G.G. Lorentz, Some new functional spaces, Ann. of Math. (2) 51 (1950), 37–55.

M. Lucia and M. Ramaswamy, Global bifurcation for semilinear elliptic problems, Recent Advances in Nonlinear Analysis, World Sci. Publ., Hackensack, NJ, 2008, pp. 197–216.

D.P. Manuel and R.F. Manásevich, Global bifurcation from the eigenvalues of the pLaplacian, J. Differential Equations 92 (1991), no. 2, 226–251.

J. Nečas, Direct Methods in the Theory of Elliptic Equations, Springer Monographs in Mathematics, Springer, Heidelberg, 2012.

K. Otared, Introductionà la Théorie des Points Critiques et Applications aux Problèmes Elliptiques, vol. 13, Springer–Verlag, Paris, 1993.

C.D. Pagani and D. Pierotti, Multiple variational solutions to nonlinear Steklov problems, NoDEA Nonlinear Differential Equations Appl. 19 (2012), no. 4, 417–436.

P.H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Funct. Anal. 7 (1971), 487–513.

P.H. Rabinowitz, Some aspects of nonlinear eigenvalue problems, Rocky Mountain J. Math. 3 (1973), 161–202.

A.J. Rumbos and A.L. Edelson, Bifurcation properties of semilinear elliptic equations in Rn , Differential Integral Equation 7 (1994), no. 2, 399–410.

I.V. Skrypnik, Methods for analysis of nonlinear elliptic boundary value problems, Translations of Mathematical Monographs, vol. 139, American Mathematical Society, Providence, RI, 1994.

W. Stekloff, Sur les problèmes fondamentaux de la physique mathématique (suite et fin), Ann. Sci. École Norm. Sup. (3) 19 (1902), 455–490.

C.A. Stuart and J.F. Toland, A global result applicable to nonlinear Steklov problems, J. Differential Equations 15 (1974), 247–268.

J.L. Vázquez, A strong maximum principle for some quasilinear elliptic equations, Appl. Math. Optim. 12 (1984), no. 3, 191–202.

M. Tian and S. Wang, Bifurcation Theory and Applications, vol. 53, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005.

O. Torné, Steklov problem with an indefinite weight for the p-Laplacian, Electron. J. Differential Equations (2005), no. 87, 8 pp.

H. Troger, Application of bifurcation theory to the solution of nonlinear stability problems in mechanical engineering, Numerical Methods for Bifurcation Problems, vol. 70, Birkhäuser, Basel, 1984, pp. 525–546.

Opublikowane

2021-12-05

Jak cytować

1.
& . Topological Methods in Nonlinear Analysis [online]. 5 grudzień 2021, T. 58, nr 2, s. 731–763. [udostępniono 22.7.2024]. DOI 10.12775/TMNA.2020.080.

Numer

Dział

Articles

Statystyki

Liczba wyświetleń i pobrań: 0
Liczba cytowań: 0