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bifurcation theory; nonlinear systems; local Lyapunov-Schmidt method

References:

[1] Abdul Hussain, M. A.: **Corner singularities of smooth functions in the analysis of bifurcations balance of the elastic beams and periodic waves**. Ph.D. thesis, Voronezh University, Russia., 2005.

[2] Abdul Hussain, M. A.: **Bifurcation solutions of elastic beams equation with small perturbation**. Int. J. Math. Anal. (Ruse) 3 (18) (2009), 879–888. MR 2604465 | Zbl 1195.74093

[3] Arnol’d, V. I.: **Singularities of differential maps**. Math. Sci. (1989).

[4] Ishibashi, Y. J.: **Phenomenological theory of domain walls**. Ferroelectrics 98 (1989), 193–205. DOI 10.1080/00150198908217582

[5] Loginov, B. V.: **Theory of Branching nonlinear equations in the conditions of invariance group**. Fan, Tashkent (1985). MR 0878356

[6] Sapronov, Y. I.: **Regular perturbation of Fredholm maps and theorem about odd field**. Works Dept. of Math., Voronezh Univ. 10 (1973), 82–88.

[7] Sapronov, Y. I.: **Nonlocal finite dimensional reduction in the variational boundary value problems**. Mat. Zametki 49 (1991), 94–103. MR 1101555

[8] Sapronov, Y. I., Darinskii, B. M., Tcarev, C. L.: **Bifurcation of extremely of Fredholm functionals**. Voronezh Univ. (2004).

[9] Sapronov, Y. I., Zachepa, V. R.: **Local analysis of Fredholm equation**. Voronezh Univ. (2002).

[10] Thompson, J. M. T., Stewart, H. B.: **Nonlinear Dynamics and Chaos**. Chichester, Singapore, J. Wiley and Sons, 1986. MR 0854476 | Zbl 0601.58001

[11] Vainbergm, M. M., Trenogin, V. A.: **Theory of branching solutions of nonlinear equations**. Math. Sci. (1969). MR 0261416