Solvability of nonlinear problem for some second-order nonstrongly elliptic system

References

• Alves CO. Existence of a positive solution for a nonlinear elliptic equation with saddle-like potential and nonlinearity with exponential critical growth in R2. Milan J Math. 2015;84(1):1–22. doi:10.1007/s00032-015-0247-9
   Web of Science ®Google Scholar
• Alves CO, Miyagaki OH, Soares SHM. Multi-bump solutions for a class of quasilinear equations on R. Commun Pure Appl Anal. 2012;11(2):829–844. doi:10.3934/cpaa.2012.11.829
   Web of Science ®Google Scholar
• Aouaoui S. Multiplicity of solutions for quasilinear elliptic equations in RN. Math Anal Appl. 2010;370:639–648. doi: 10.1016/j.jmaa.2010.04.052
   Web of Science ®Google Scholar
• Bartsch T, Pankov A, Wang ZQ. Nonlinear Schrödinger equations with steep potential well. Commun Contemp Math. 2001;3(4):549–569. doi: 10.1142/S0219199701000494
   Web of Science ®Google Scholar
• Gazzola F, Radulescu V. A nonsmooth critical point theory approach to some nonlinear elliptic equations in RN. Differ Integral Equ. 2000;13(1–3):47–60.
   Google Scholar
• Liang S, J Zhang J. Existence of multi-bump solutions for a class of quasilinear Schrödinger equations in RN involving critical growth. Milan J Math. 2015;83(1):55–90. doi:10.1007/s00032-015-0236-z
   Web of Science ®Google Scholar
• Ospanov K. L1 -maximal regularity for quasilinear second order differential equation with damped term. El J Qualit Theo Differ Equ. 2015;39:1–9.
   Google Scholar
• Ospanov K. Separation and the existence theorem for second order nonlinear differential equation. El J Qualit Theo Differ Equ. 2012;1:1–12.
   Google Scholar
• Su J. Quasilinear elliptic equations on RN with singular potentials and bounded nonlinearity. Zeitschrift für Angewandte Mathematik und Physik. 2012;63(1):51–62. doi:10.1007/s00033-011-0138-z
   Web of Science ®Google Scholar
• Lanza de Cristoforis M, Musolino P. Asymptotic behaviour of the solutions of a nonlinear Robin problem for the Laplace operator in a domain with a small hole: a functional analytic approach. Comp Var Ell Equ. 2007;52(10–11):945–977. doi: 10.1080/17476930701485630
   Google Scholar
• Lanza de Cristoforis M, Musolino P. A singularly perturbed nonlinear Robin problem in a periodically perforated domain: a functional analytic approach. Comp Var Ell Equ. 2013;58(4):511–536. doi: 10.1080/17476933.2011.638716
   Web of Science ®Google Scholar
• Tovmasyan NE. The Poincaré problem with shift for irregular second order elliptic equations. Mat Mezh Ross-Kaz Symp; Nalchik-Elbrus: 2004. p. 170–172 (in Russian).
   Google Scholar
• Tovmasyan NE, Babayan AO. The Dirichlet problem for second order elliptic systems in the class of the functions with polynomial growth. Mat Mezh Ross-Kaz Symp.; Nalchik-Elbrus: 2004. p. 172–174 (in Russian).
   Google Scholar
• Soldatov AP. The Dirichlet and Neumann problems for second order elliptic systems in the halfplane. Tez Mezhd Confer‘Dif Urav smezh vopr’; Moscow: 2004. p. 218–219.
   Google Scholar
• Soldatov AP. Second-order elliptic systems in the half-plane. (English. Russian original) Izv Math. 2006;70(6):1233–1264; translation from Izv Ross Akad Nauk, Ser Mat. 2006;70(6):161–192.
   Google Scholar
• Soldatov AP. On representation of solutions of second order elliptic systems in the plane. In: Begehr HGW, Nicolosi F, editors. More progresses in analysis. Proceedings of the 5th international ISAAC congress; 2005 Jul 25–30; Catania, Italy. Hackensack (NJ): World Scientific (ISBN 978-981-283-562-8/hbk); 2009. p. 1171–1184.
   Google Scholar
• Soldatov AP. The Neumann problem for elliptic systems on a plane. J Math Sci. 2014;202(6):897–910. doi: 10.1007/s10958-014-2085-7
   Google Scholar
• Vishik MI. On strongly elliptic systems of differential equations. Mat Sbornik. 1951;29:615–676. (in Russian).
   Google Scholar
• Lopatinskiy Ya.B. A method of reducing the boundary-value problems for a system of elliptic differential equations to regular integral equations. Ukr Mat Zhurn. 1953;0(2):123–151. (in Russian)
   Google Scholar
• Bitsadze AV. On the uniqueness of the solutions of the Dirichlet problem for elliptic partial differential equations. Ukr Mat Zhur. 1948;3(6):211–212 (in Russian)
   Google Scholar
• Bitsadze AV. Boundary value problems for second order elliptic equations. Amsterdam: North-Holland; 1968.
   Google Scholar
• Ospanov KN. Coercive estimates for a degenerate elliptic system of equations with spectral applications. Appl Math Lett. 2011;24(9):1594–1598. doi: 10.1016/j.aml.2011.04.006
   Web of Science ®Google Scholar
• Ospanov KN. On nonlinear generalized Cauchy-Riemann system on the whole plane. Siberian Math J. 1997;38(2):314–319. doi: 10.1007/BF02674630
   Web of Science ®Google Scholar
• Zhapsarbayeva L. On approximation properties of second order singular degenerate elliptic systems in L2. Complex Var Ell Equ. 2013;58(2):197–220. doi: 10.1080/17476933.2011.563848
   Web of Science ®Google Scholar
• Ladyzhenskaya OA, Uraltseva NN. Linear and quasilinear elliptic equations. New York (NY): Academic press; 1968.
   Google Scholar
• Petrovskii IG. Partial differential equations. London: Iliffe Books Ltd; 1967.
   Google Scholar
• Ladyzhenskaya OA. Boundary value problems of mathematical physics. Vol. 408, Moscow: Nauka; 1973. (in Russian).
   Google Scholar
• Everitt WN, Giertz M. On some properties of the powers of a formally selfadjoint differential expression. Proc London Math Soc. 1972;24(3):149–170. doi: 10.1112/plms/s3-24.1.149
   Google Scholar
• Everitt WN, Giertz M. Some properties of the domains of certain differential operators. Proc London Math Soc. 1971;23(3):301–324. doi: 10.1112/plms/s3-23.2.301
   Google Scholar
• Otelbayev M. On the Titchmarsch method of estimating the resolvent. Dokl Akad Nauk SSSR. 1973;211(4):787–790. (in Russian)
   Google Scholar
• Otelbayev M. On the separability of the elliptic operators. Dokl Akad Nauk SSSR. 1977;243(3):540–543. (in Russian).
   Google Scholar
• Otelbayev M. Nonlocal estimates of the derivatives of solutions of the elliptic equations in unbounded domains. Prepr. Inst. Mat. Sib. Otd. Akad. Nauk SSSR; 1979. (in Russian).
   Google Scholar
• Otelbayev M. Coercivity estimates and separability theorems of elliptic equations. Tr Mat Inst AN SSSR. 1983;161:195–217. (in Russian).
   Google Scholar
• Oinarov R. The separability of the Schrödinger operator in the space of summable functions. Dokl Akad Nauk SSSR. 1985;285(5):1062–1064. (in Russian).
   Google Scholar
• Mynbayev K, Otelbayev M. Weighted functional spaces and differential operator spectrum. Moscow: Nauka; 1988. (in Russian).
   Google Scholar
• Kantorovich LN, Akilov GP. Functional analysis in normed spaces. Vol. 773, New York (NY): Pergamon Press Ltd; 1964.
   Google Scholar