Solvability Conditions for Some Systems of Nonlinear Non-Fredholm Elliptic Equations
DOI:
https://doi.org/10.5890/DNC.2013.04.005Abstract
We establish the existence and uniqueness of standing solitary wavelike solutions in H2 for certain systems of nonlocal nonlinear equations. These problems involve second order differential operatorswithout Fredholm property.References
[1] Pelinovsky, D.E. and Yang, J. (2002), A normal form for nonlinear resonance of embedded solitons, The Royal Society of London. Proceedings. Series A. Mathematical, Physical and Engineering Sciences, 458( 2022), 1469- 1497.
[2] Cuccagna, S., Pelinovsky, D., and Vougalter, V. (2005), Spectra of positive and negative energies in the linearized NLS problem, Communications on Pure and Applied Mathematics, 58(1), 1-29.
[3] Vougalter, V. (2010), On threshold eigenvalues and resonances for the linearized NLS equation, Mathematical Modelling of Natural Phenomena, 5 (4), 448-469.
[4] Vougalter, V., Volpert, V. (2012), Solvability conditions for some linear and nonlinear non-Fredholm elliptic problems, Analysis and Mathematical Physics, 2(4), 473-496.
[5] Volpert, V., Kazmierczak, B., Massot, M., and Peradzynski, Z. (2002), Solvability conditions for elliptic problems with non-Fredholm operators, Applicationes Mathematicae, 29 (2), 219-238.
[6] Vougalter, V. and Volpert, V. (2011), Solvability conditions for some non Fredholm operators, Proceedings of the Edinburgh Mathematical Society, (2) 54(1), 249-271.
[7] Vougalter, V. and Volpert, V. (2010), On the solvability conditions for some non Fredholm operators, International Journal of Pure and Applied Mathematics, 60 (2), 169-191.
[8] Vougalter, V. and Volpert, V. (2012) On the solvability conditions for the diffusion equation with convection terms, Communications on Pure and Applied Analysis, 11 (1), 365-373.
[9] Vougalter, V. and Volpert, V. (2010), Solvability relations for some non Fredholm operators, International Electronic Journal of Pure and Applied Mathematics, 2(1), 75-83.
[10] Volpert, V. and Vougalter, V. (2011), On the solvability conditions for a linearized Cahn-Hilliard equation, Rendiconti dell'Istituto di Matematica dell'Universitàdi Trieste, 43 , 1-9.
[11] Vougalter, V., Volpert, V. (2012), Solvability conditions for a linearized Cahn-Hilliard equation of sixth order, Mathematical Modelling of Natural Phenomena, 7(2), 146-154.
[12] Ducrot, A., Marion, M., and Volpert, V. (2005), Systemes de réaction-diffusion sans propriété de Fredholm, Comptes Rendus Mathematique, 340(9), 659-664.
[13] Ducrot, A., Marion, M., and Volpert, V. (2008), Reaction-diffusion problems with non Fredholm operators, Advances in Differential Equations, 13 (11-12), 1151-1192.
[14] Ducrot, A., Marion, M., and Volpert, V. (2009), Reaction- Diffusion Waves (with the Lewis Number Different From 1), Publibook, Paris.
[15] Vougalter, V. and Volpert, V. (2011), On the existence of stationary solutions for some non-Fredholm integrodifferential equations, Documenta Mathematica, 16, 561-580.
[16] Volpert, V. and Vougalter, V. (2012), On the existence of stationary solutions for some systems of non-Fredholm integro-differential equations, Discontinuity, Nonlinearity and Complexity, 1(2), 85-98.
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