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Perturbations of second order linear elliptic problems by unbounded nonlinearities. (English) Zbl 0509.35035

MSC:
35J65Nonlinear boundary value problems for linear elliptic equations
35J25Second order elliptic equations, boundary value problems
47A53(Semi-) Fredholm operators; index theories
55M20Fixed points and coincidences (algebraic topology)
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Full Text: DOI
References:
[1] Bers, L.; John, F.; Schechter, M.: Partial differential equations. (1964) · Zbl 0126.00207
[2] BrĂ©zis, H.; Nirenberg, L.: Characterizations of the ranges of some nonlinear operators and applications to boundary value problems. Annali scu. Norm. sup. Pisa, ser IV 5, 225-326 (1978) · Zbl 0386.47035
[3] De Figueiredo, D. G.; Gossez, J. P.: Nonlinear perturbations of a linear elliptic problem near its first eigenvalue. J. diff. Eqns 30, 1-19 (1978) · Zbl 0357.35036
[4] De Figueiredo, D. G.; Ni, W. M.: Perturbations of second order linear elliptic problems by nonlinearities without landesman-lazer condition. Nonlinear analysis 3, 629-634 (1979) · Zbl 0429.35035
[5] Gupta, C. P.: On functional equations of Fredholm and Hammerstein type with applications to existence of periodic solutions of certain ordinary differential equations. J. integral eqns 3, 21-41 (1981) · Zbl 0457.34040
[6] Gupta, C. P.; Hess, P.: Existence theorems for nonlinear noncoercive operator equations and nonlinear elliptic boundary value problems. J. diff. Eqns 22, 305-313 (1976) · Zbl 0344.47027
[7] Fucik, S.; Krebec, M.: Boundary value problems with bounded nonlinearity and general null space of the linear part. Math. Z. 155, 129-138 (1977) · Zbl 0337.35034
[8] Hess, P.: A remark in the preceding paper of Fucik and krebec. Math. Z. 155, 139-141 (1977) · Zbl 0356.35030
[9] Landesman, E. M.; Lazer, A. C.: Nonlinear perturbations of linear elliptic boundary value problems at resonance. J. math. Mech. 19, 609-623 (1970) · Zbl 0193.39203
[10] Mawhin, J.: Landesman-lazer type problems for nonlinear equations. Conf. sem. Mat. univ. Bari (1977) · Zbl 0436.47050
[11] Mawhin, J.: Topological degree methods in nonlinear boundary value problems. CBMS regional conference series in maths. Number 40 (1979)