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Boundary value problems with bounded nonlinearity and general null-space of the linear part. (English) Zbl 0337.35034
MSC:
35J65Nonlinear boundary value problems for linear elliptic equations
35B45A priori estimates for solutions of PDE
References:
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[2]Browder, F.E.: Estimates and existence theorems for elliptic boundary value problems. Proc. nat. Acad. Sci. USA45, 365–372 (1959) · Zbl 0093.29402 · doi:10.1073/pnas.45.3.365
[3]Dancer, E.N.: On the Dirichlet problem for weakly nonlinear elliptic partial differential equations. Proc. Royal Soc. Edinburgh. Will appear in Proc. Royal Soc. Edinburgh
[4]Fučík, S.: Nonlinear equations with noninvertible linear part. Czechosl. math. J.24, 467–495 (1974)
[5]Fučík, S.: Further remark on a theorem by E.M. Landesman and A.C. Lazer. Commentationes math. Univ. Carolinae15, 259–271 (1974)
[6]Fučík, S.: Remarks on some nonlinear boundary value problems. Commentationes math. Univ. Carolinae17, 721–730 (1976)
[7]Fučík, S., Kučera, M., Nečas, J.: Ranges of nonlinear asymptotically linear operators. J. diff. Equations17, 375–394 (1975) · Zbl 0299.47035 · doi:10.1016/0022-0396(75)90050-9
[8]Kazdan, J.L., Warner, F.W.: Remarks on some quasilinear elliptic equations. Comm. pure appl. Math.28, 567–597 (1975) · Zbl 0325.35038 · doi:10.1002/cpa.3160280502
[9]Krbec, M.: OnL p-estimates for solutions of elliptic boundary value problems. Commentationes math. Univ. Crrolinae17, 363–375 (1976)
[10]Landesman, E.M., Lazer, A.C.: Nonlinear perturbations of linear boundary value problem at resonance, J. Math. Mech.19, 609–623 (1970)
[11]Nečas, J.: Les Méthodes Directes en Théorie des Équations Elliptiques. Prague: Academia 1967
[12]Nečas, J.: Sur la régularité des solutions variationnelles des équations elliptiques non-linéaires d’ordre 2k en deux dimensions. Ann. Scuola norm. sup. Pisa, Sci fis. mat., III Ser.21, 427–457 (1967)
[13]Nečas, J.: On the range of nonlinear operators with linear asymptotes which are not invertible. Commentationes math. Univ. Carolinae14, 63–72 (1973)
[14]Williams, S.A.: A sharp sufficient condition for solution of a nonlinear elliptic boundary value problem. J. diff. Equations8, 580–586 (1970) · Zbl 0209.13003 · doi:10.1016/0022-0396(70)90031-8