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Variational methods for non-differentiable functionals and their applications to partial differential equations. (English) Zbl 0487.49027


MSC:

49Q20 Variational problems in a geometric measure-theoretic setting
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
28A15 Abstract differentiation theory, differentiation of set functions
26B35 Special properties of functions of several variables, Hölder conditions, etc.
35J60 Nonlinear elliptic equations
35R05 PDEs with low regular coefficients and/or low regular data
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[1] Ahmad, S; Lazer, A.C; Paul, J.L, Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Indiana univ. J., 25, 933-944, (1976) · Zbl 0351.35036
[2] Amann, H, Ljusternik-schmirelmann theory and nonlinear eigenvalue problem, Math. ann., 199, 55-72, (1972)
[3] Ambrosetti, A; Rabinowitz, P.H, Dual variational methods in critical point theory and applications, J. functional analysis, 14, 349-381, (1973) · Zbl 0273.49063
[4] {\scV. Benci and P. H. Rabinowitz}, Critical point theorems for indefinite functionals. · Zbl 0465.49006
[5] Browder, F, Variational methods for nonlinear elliptic eigenvalue problems, Bull. amer. math. soc., 71, 174-183, (1965) · Zbl 0135.15802
[6] Chang, K.C, On the multiple solutions of the elliptic differential equations with discontinuous nonlinear terms, Sci. sinica, 21, 139-158, (1978) · Zbl 0397.35057
[7] {\scK. C. Chang}, The obstacle problem and partial differential equations with discontinuous nonlinearities, to appear. · Zbl 0405.35074
[8] Chang, K.C; Jiang, B.J, Fixed point index of the set-valued mappings and multiplicity of solutions of elliptic equations with discontinuous nonlinearities, Acta math. sinica, 21, 26-43, (1978) · Zbl 0378.35026
[9] Chang, K.C; Jiang, L.S, The free boundary problems of the stationary water cone, Acta sci. natur. univ. peking, 1-25, (1978)
[10] Clark, D.C, A variant of the Ljusternik-schmirelmann theory, Indiana univ. math. J., 22, 65-74, (1972)
[11] Clarke, F.H, A new approach to Lagrange multipliers, Math. oper. res., 1, 165-174, (1976) · Zbl 0404.90100
[12] Fleishman, B.A; Mahar, T.J, Analytic methods for approximate solution of elliptic free boundary problems, Nonlinear analysis, 1, 561-569, (1979) · Zbl 0386.65050
[13] Massabo, I, Positive eigenvalues for elliptic equations with discontinuous nonlinearities, Bumi, 5, 814-827, (1978) · Zbl 0393.35050
[14] Massabo, I; Stuart, C.A, Elliptic eigenvalue problems with discontinuous nonlinearities, J. math. anal. appl., 66, 261-281, (1978) · Zbl 0408.35070
[15] McKenna, P.J, Discontinuous perturbations of elliptic boundary value problems at resonance, nonlinear equations in abstract spaces, (), 375-386
[16] Ni, W.M, Some minimax principles with applications in nonlinear elliptic boundary value problems and global vortex flow, Doctoral thesis, (1979)
[17] Pohozaev, S.I, Eigenfunctions of the equation δu + λf(u) = 0, Soviet math. dokl., 5, 1408-1411, (1965) · Zbl 0141.30202
[18] Rabinowitz, P, Variational methods for nonlinear eigenvalue problems, CIME varenora, 1-56, (1974)
[19] Rabinowitz, P, A minimax principle and applications to elliptic partial differential equations, (), 97-115
[20] Rabinowitz, P, Some minimax theorems and applications to nonlinear partial differential equations, Nonlinear analysis, 161-177, (1978)
[21] Rauch, J, Discontinuous semilinear differential equations and multiple valued maps, (), 277-282 · Zbl 0413.35031
[22] {\scC. A. Stuart and J. F. Toland}, A variational method for boundary value problems with discontinuous nonlinearities, preprint. · Zbl 0434.35042
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