Nontrivial solutions to boundary value problems for semilinear degenerate elliptic differential equations, I
Người báo cáo: Dương Trọng Luyện (Đại học Hoa Lư)

Thời gian: 10h00, Thứ Tư, ngày 6/7//2022

Địa điểm: Phòng Semina tầng 5, tòa nhà A6, Viện Toán học.

Tóm tắt: In this talk, we study boundary value problems for semi-linear equations involving degenerate elliptic differential operators. Via a Pohozaev’s type identity we show that if the nonlinear term grows faster than some power function then the boundary value problem has no nontrivial solution. Otherwise when the nonlinear term grows slower than the same power function, by establishing embedding theorems for weighted Sobolev spaces associated with the degenerate elliptic equations, then applying the theory of critical values in Banach spaces, we prove that the problem has a nontrivial solution, or even infinite number of solutions provided that the nonlinear term is an odd function.


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