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


Zhapsarbayeva L. Ospanov K.
2021Taylor and Francis Ltd.

Complex Variables and Elliptic Equations
2021#66Issue 6-71073 - 1083 pp.

In this work, we investigate the second-order nonlinear elliptic system defined on an unbounded domain and with variable nonconstant coefficients. We establish the existence of the solution of the nonlinear problem for a second-order nonstrongly elliptic system by using a coercive estimate, which is obtained for the linear case. The nonlinear elliptic system is transformed into an equivalent fixed point problem for a suitable nonlinear operator in a convex subset of a Banach function space. Using the topological fixed-point approach and embedding theorems, the conditions for solvability of the semiperiodical nonlinear problem in a weighted Sobolev space are obtained.

35J47 , 35J50 , 35J57 , 35J60 , 35J75 , boundary value problems for second-order elliptic systems , Nonlinear elliptic equations , second-order elliptic systems , singular elliptic equations , weighted Sobolev space

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Department of Differential Equations and Control Theory, al-Farabi Kazakh National University, Almaty, Kazakhstan
Department of Fundamental Mathematics, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan

Department of Differential Equations and Control Theory
Department of Fundamental Mathematics

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