Componentwise localization of critical points for functionals defined on product spaces
DOI:
https://doi.org/10.12775/TMNA.2021.007Słowa kluczowe
Critical point, linking, minimum point, saddle point, minimax theorem, gradient type systemAbstrakt
A new notion of linking is introduced to treat minima as minimax points in a unitary way. Critical points are located in conical annuli making possible to obtain multiplicity. For functionals defined on a Cartesian product, the localization of critical points is given on components and the variational properties of the components can differ, part of them being of minimum type, others of mountain pass type.Bibliografia
H. Brezis and L. Nirenberg, Remarks on finding critical points, Comm. Pure Appl. Math. 44 (1991), 939–964.
D.G. De Figueiredo, Lectures on the Ekeland Variational Principle with Applications and Detours, Tata Institute of Fundamental Research, Bombay, 1989.
K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985.
Y. Jabri, The Mountain Pass Theorem, Cambridge Univ. Press, 2003.
J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer, New York, 1989.
S.G. Mikhlin, Linear Partial Differential Equations, Vysshaya Shkola, Moscow, 1977 (Russian).
R. Precup, Critical point theorems in cones and multiple positive solutions of elliptic problems, Nonlinear Anal. 75 (2012), 834–851.
R. Precup, On a bounded critical point theorem of Schechter, Stud. Univ. Babeş-Bolyai Math. 58 (2013), 87–95.
R. Precup, A variational analogue of Krasnosel’skiı̆’s cone fixed point theory, Nonlinear Analysis and Boundary Value Problems (I. Area et al., eds.), Springer Proceedings in Mathematics & Statistics, vol. 292, Springer, 2019, pp. 1–18.
R. Precup, P. Pucci and C. Varga, Energy-based localization and multiplicity of radially symmetric states for the stationary p-Laplace diffusion, Complex Var. Elliptic Equ. 65 (2020), 1198–1209.
R. Precup and C. Varga, Localization of positive critical points in Banach spaces and applications, Topol. Methods Nonlinear Anal. 49 (2017), 817–833.
P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conference Series Math., vol. 65, Amer. Math. Soc., Providence, 1986.
M. Schechter, Linking Methods in Critical Point Theory, Birkhäuser, Boston, 1999.
M. Struwe, Variational Methods, Springer, Berlin, 1990.
E. Zeidler, Applied Functional Analysis: Applications to Mathematical Physics, Springer, Berlin, 1995.
M. Willem, Minimax Theorems, Progress in Nonlinear Differential Equations and Their Applications, vol. 24, Birkhäuser, Boston, 1996.
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Prawa autorskie (c) 2021 Topological Methods in Nonlinear Analysis
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