References

  1. Appell J., De Pascale E., Vignoli A. Nonlinear Spectral Theory. In: Appell J. (Ed.) Germany De Gruyter Series in Nonlinear Analysis and Applications, 10. Walter de Gruyter, Germany, 2004.
  2. Appell J., Dörfner M. Some spectral theory for nonlinear operators. Nonlinear Anal. 1997, 28 (12), 1955–1976. doi:10.1016/S0362-546X(96)00040-5
  3. Armstrong S.N. Principal eigenvalues and an anti-maximum principle for homogeneous fully nonlinear elliptic equations. J. Differential Equations 2009, 246 (7), 2958–2987. doi:10.1016/j.jde.2008.10.026
  4. Azzollini A., d’Avenia P., Pomponio A. Multiple critical points for a class of nonlinear functionals. Ann. Mat. Pura Appl. (4) 2011, 190, 507–523.
  5. Barroso C.S. Semilinear Elliptic Equations and Fixed Points. Proc. Amer. Math. Soc. 2004, 133 (3), 745–749. doi:10.1090/S0002-9939-04-07718-4
  6. Berger M.S. A Strum-Liouville theorem for nonlinear elliptic partial differential equations. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 1966, 20 (3), 543–582.
  7. Brezis H. Functional analysis, Sobolev spaces and partial differential equations. In: Berestycki N., Casacuberta C., Greenlees J., MacIntyre A., Sabbah C., Süli E. (Eds.) Universitext. Springer, New York, 2011.
  8. Brézis H. Équations et inéquations non linéaires dans les espaces vectoriels en dualité. Ann. Inst. Fourier (Grenoble) 1968, 18 (1), 115–175. (in French)
  9. Browder F.E. Nonlinear Eigenvalue Problems and Galerkin Approximations. Bull. Amer. Math. Soc. 1968, 74, 651–656.
  10. Browder F.E. Variational methods for nonlinear elliptic eigenvalue problems. Bull. Amer. Math. Soc. 1965, 71, 176–183. doi:10.1090/S0002-9904-1965-11275-7
  11. Browder F.E. Infinite dimensional manifolds and nonlinear elliptic eigenvalue problems. Ann. of Math. (2) 1965, 82, 459–477.
  12. Bungert L., Burger M., Chambolle A., Novaga M. Nonlinear Spectral Decompositions by Gradient Flows of One-Homogeneous Functionals. Anal. PDE 2021, 14 (3), 823–860. doi:10.2140/apde.2021.14.823
  13. Calamai A., Furi M., Vignoli A. A new spectrum for nonlinear operators in Banach spaces. Nonlinear Funct. Anal. Appl. 2009, 14 (2), 317–347. doi:10.48550/arXiv.1005.1819
  14. Chipot M., Weissler F. On the Elliptic Problem \(\Delta u-\left\vert \nabla u\right\vert ^{q}+\lambda u^{p}=0\). In: Ni W.M., Peletier L.A., Serrin J. Nonliner Diffusion Equations and their equilibruim states I. Berkeley, CA, Math Sci. Res. Inst. Publ. 1986, 12, Springer, New York, 237–243.
  15. Costea N., Mihăilescu M. Nonlinear, degenerate and singular eigenvalue problems on \(R^{n}\). Nonlinear Anal. 2009, 71 (3–4), 1153–1159. doi:10.1016/j.na.2008.11.041
  16. Crandal M.G., Rabinowitz P.H. Bifurcation from simple eigenvalues. J. Funct. Anal. 1971, 8 (2), 321–340. doi:10.1016/0022-1236(71)90015-2
  17. Dugundji J. An extension of Tietze’s theorem. Pacific J. Math. 1951, 1 (3), 353–367. doi:10.2140/pjm.1951.1.353
  18. Feng W. A new spectral theory for nonlinear operators and its applications. Abstr. Appl. Anal. 1997, 2 (1–2), 163–183.
  19. Furi M., Martelli M., Vignoli A. Contributions to spectral theory for nonlinear operators in Banach spaces. Ann. Mat. Pura Appl. (4) 1978, 118, 229–294. doi:10.1007/BF02415132
  20. Hildebrandt S. Über die Lösung nichtlinearer Eigenwertaufgaben mit der Gölerkinverfahren. Math. Z. 1967, 101, 255–264. (in German)
  21. Kang Sh., Zhang Y., Feng W. Nonlinear Spectrum and Fixed Point Index for a Class of Decomposable Operators. Mathematics 2021, 9 (3), 278. doi:10.3390/math9030278
  22. Kachurovskij R.I. Regular points, spectrum and eigenfunctions of nonlinear operators. Dokl. Akad. Nauk USSR 1969, 188, 274–277. (translation of Soviet Math. Dokl. 1969, 10, 1101–1105. (in Russian))
  23. Keller J.B., Antman S. Bifurcation Theory and Nonlinear Eigenvalue Problems. Benjamin, New York, 1969.
  24. Lindqvist P. On the equation \(\mathrm{div}\left( \left\vert \nabla u\right\vert ^{p-2}\nabla u\right) +\lambda \left\vert u\right\vert^{p-2}u=0\). Proc. Amer. Math. Soc. 1990, 109 (1), 157–164.
  25. Lopez-Gomez J. Spectral Theory and Nonlinear Functional Analysis. Chapman and Hall/CRC, New York, 2001. doi:10.1201/9781420035506
  26. Neuberger J.W. Existence of a spectrum for nonlinear transformations. Pacific J. Math. 1969, 31 (1), 157–159. doi:10.2140/pjm.1969.31.157
  27. Rabinowitz P.H. Some global results for nonlinear eigenvalue problems. J. Funct. Anal. 1971, 7, 487–513. doi:10.1016/0022-1236(71)90030-9
  28. Rhodius A. Der numerische Wertebereich und die Lösbarkeit linearer und nichtlinearer Operatorengleichungen. Math. Nachr. 1977, 79 (1), 343–360. (in German) doi:10.1002/mana.19770790137
  29. Santucci P., Väth M. On the definition of eigenvalues for nonlinear operators. Nonlinear Anal. 2000, 40 (1–8), 565–576. doi:10.1016/S0362-546X(00)85034-8
  30. Soltanov K.N. Nonlinear mappings and the solvability of nonlinear equations. Soveit. Math. Dokl. 1987, 34 (1), 242–246.
  31. Soltanov K.N. Nonlinear Operators, Fixed-Point Theorems, Nonlinear Equations. In: Mityushev V.V., Ruzhansky M.V. (Eds.) Trends in Mathematics, Current Trends in Analysis and Its Applications, Proc. of the 9th ISAAC Congress, Krakow, Poland, 2013, Springer, 2015, 347–360. doi:10.1007/978-3-319-12577-0_41
  32. Soltanov K.N. Some applications of nonlinear analysis to differential equations. ELM, Baku, 2002. (in Russian)
  33. Soltanov K.N. On equations with continuous mappings in Banach spaces. Funct. Anal. Appl. 1999, 33 (1), 76–81.
  34. Soltanov K.N. On semi-continuous mappings, equations and inclusions in the Banach space. Hacet. J. Math. Stat. 2008, 37 (1), 9–24.
  35. Soltanov K.N. Perturbation of the mapping and solvability theorems in the Banach space. Nonlinear Anal. 2010, 72, 164–175. doi:10.1016/J.NA.2009.06.067
  36. Soltanov K.N. On noncoercive semilinear equations. Nonlinear Anal. Hybrid Syst. 2008, 2 (2), 344–358.
  37. Vainberg M.M. Variational Methods for the investigation of non-linear operators. GITTL, Moscow, 1959.
  38. Zeidler E. Nolinear Functional Analysis and its Applications II/B: Nonlinaer Monotone Operators. Springer-Verlag, Berlin, 1990.
  39. Huang Y.Xi. On Eigenvalue Problems of the p-Laplacian with Neumann Boundary Conditions. Proc. Amer. Math. Soc. 1990, 109 (1), 177–184. doi:10.2307/2048377