Abstract
Let us give the following simple motivation which arises in such a fundamental subject as the Sobolev imbedding theorems.
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References
R.A. AdamsSobolev SpacesAcademic Press Inc., New York, 1975.
A. Anane, Simplicité et isolation de la premiére valeur propre du p—Laplacien avec poidsC.R. Acad. Sci. Paris Sér. I. Math. 305 (1987), 725–728.
A. Anane and N. Tsouli, On the second eigenvalue of the p-Laplacian. In:Nonlinear Partial Differential Equations(From a Conference in Fes, Maroc, 1994) (A. Benkirane and J.-P. Grossez ed.), Pitman Research Notes in Math. 343, Longman, 1996.
P. Binding, P. Drábek and Y.X. Huang, On the Fredholm alternative for the p-LaplacianProc. Amer. Math. Soc. 125(1997), 3555–3559.
M. DelPino, P. Drábek and Manásevich, The Fredholm alternative at the first eigenvalue for the one dimensional p-LaplacianJ. Differential Equations 159 (1999), 386–419.
M.A. DelPino, M. Elgueta and R. Manásevich, A homotopic deformation alongpof a Leray—Schauder degree result and existence for,J. Differential Equations 80(1989), 1–13.
M. DelPino and R. Manásevich, Multiple solutions for the p-Laplacian under global nonresonanceProc. Amer. Math. Soc. 112(1991), 131–138.
P. Drábek, Ranges of a-homogeneous operators and their perturbationsCasopis pro Péstování Matematiky 105(1980), 167–183.
P. Drábek, A note on the nonuniqueness for some quasilinear eigen-value problemAppl. Math. Letters 13(2000), 39–41.
P. Drábek and R. Manásevich, On the closed solution to some non-homogeneous eigenvalue problems with p-LaplacianDifferential and Integral Equations 12(1999), 773–788.
P. Drábek and P. Takác, A counterexample to the Fredholm alternative for the p-LaplacianProc. Amer. Math. Society 127(1999), 1079–1087.
J. Fleckinger, J. Hernández, P. Takác and F. deThélin, Uniqueness and positivity for solutions of equations with the p-Laplacian. In:Proceedings of the Conference on Reaction - Diffusion EquationsTrieste, Italy, October 1985. Marcel Dekker, Inc., New York, Basel, 1997.
J. García and I. Peral, Existence and non-uniqueness for the p-Laplacian: Non-linear eigenvaluesComm. Partial Differential Equations 12(1987), 1389–1430.
J. García and I. Peral, On limits of solutions of elliptic problems with nearly critical exponentComm. Partial Differential Equations17 (1992), 2113–2126.
Y.X. Huang, A note on the asymptotic behavior of positive solutions for some elliptic equationNonlinear Analysis T.M.A.29 (1997), 533–537.
A. Kufner, O. John and S. FucíkFunction SpacesAcademia, Prague, 1977.
P. Lindqvist, On the equation divProc.Amer. Math. Soc.109 (1990), 157–164.
M. Otani, A remark on certain nonlinear elliptic equationsProc. Fac. Tokai Univ.XIX (1984), 23–28.
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Drábek, P. (2001). Some Aspects of Nonlinear Spectral Theory. In: Grossinho, M.R., Ramos, M., Rebelo, C., Sanchez, L. (eds) Nonlinear Analysis and its Applications to Differential Equations. Progress in Nonlinear Differential Equations and Their Applications, vol 43. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0191-5_15
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DOI: https://doi.org/10.1007/978-1-4612-0191-5_15
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