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
10 лет помогаем публиковать статьи Международный издатель
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