## Solvability of semilinear equations with compact perturbations of operators of monotone type

HTML articles powered by AMS MathViewer

- by Zhengyuan Guan PDF
- Proc. Amer. Math. Soc.
**121**(1994), 93-102 Request permission

## Abstract:

The solvability of the equation $Au - Tu + Cu = f$ is studied under various assumptions of monotonicity and compactness on the operators*A, T*, and

*C*, which map subsets of a reflexive Banach space

*X*into its dual space. It is nowhere assumed that

*X*possesses a Schauder basis or that the operator

*T*is positive definite and selfadjoint. The results extend and/or improve recent results obtained by Chen, Kartsatos and Mabry, and Kesavan.

## References

- Nicholas D. Alikakos and Rouben Rostamian,
*Lower bound estimates and separable solutions for homogeneous equations of evolution in Banach space*, J. Differential Equations**43**(1982), no. 3, 323–344. MR**649843**, DOI 10.1016/0022-0396(82)90081-X - Felix E. Browder,
*Fixed point theory and nonlinear problems*, Bull. Amer. Math. Soc. (N.S.)**9**(1983), no. 1, 1–39. MR**699315**, DOI 10.1090/S0273-0979-1983-15153-4 - Felix E. Browder and Bui An Ton,
*Convergence of approximants by regularization for solutions of nonlinear functional equations in Banach spaces*, Math. Z.**106**(1968), 1–16. MR**239472**, DOI 10.1007/BF01137968 - Yong Zhuo Chen,
*Solvability of nonlinear perturbations of linear operator equations with parameters*, Appl. Anal.**44**(1992), no. 3-4, 209–222. MR**1284999**, DOI 10.1080/00036819208840079 - Philippe G. Ciarlet and Patrick Rabier,
*Les équations de von Kármán*, Lecture Notes in Mathematics, vol. 826, Springer, Berlin, 1980 (French). MR**595326**
Z. Guan, - Athanassios G. Kartsatos and Richard D. Mabry,
*On the solvability in Hilbert space of certain nonlinear operator equations depending on parameters*, J. Math. Anal. Appl.**120**(1986), no. 2, 670–678. MR**864783**, DOI 10.1016/0022-247X(86)90188-5 - S. Kesavan,
*Existence of solutions by the Galerkin method for a class of nonlinear problems*, Applicable Anal.**16**(1983), no. 4, 279–290. MR**718535**, DOI 10.1080/00036818308839475 - N. G. Lloyd,
*Degree theory*, Cambridge Tracts in Mathematics, No. 73, Cambridge University Press, Cambridge-New York-Melbourne, 1978. MR**0493564**
P. S. Milojević, - P. S. Milojević,
*Solvability of semilinear equations with strong nonlinearities and applications to elliptic boundary value problems*, Comment. Math. Univ. Carolin.**28**(1987), no. 4, 735–750. MR**928686**
D. Pascali and J. Sburlan,

*On operators of monotone type in Banach space*, Ph.D. Dissertation, Univ. South Florida, Tampa, FL, 1990.

*Solvability of some semilinear equations with strong nonlinearities and application to elliptic problems*, Appl. Anal.

**25**(3) (1987), 181-196.

*Nonlinear mappings of monotone type*, Sijthoff and Noordhoof, Bucharest, 1978.

## Additional Information

- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**121**(1994), 93-102 - MSC: Primary 47H15; Secondary 47H05, 47H11
- DOI: https://doi.org/10.1090/S0002-9939-1994-1174492-4
- MathSciNet review: 1174492