论文信息 - Positive Solutions for Nonlinear Eigenvalue Problems

Positive Solutions for Nonlinear Eigenvalue Problems

Ž . We are concerned with determining values of l eigenvalues , for which there exist positive solutions of the boundary value problem u q la t f u s 0, 0 t 1, 1l Ž . Ž . Ž . u 0 s u 1 s 0, 2 Ž . Ž . Ž . where Ž . w . w . A f : 0, ` a 0, ` is continuous, Ž . w x w . B a: 0, 1 a 0, ` is continuous and does not vanish identically on any subinterval, and Ž . Ž Ž . . Ž Ž . . q C f s lim f x rx and f s lim f x rx exist. 0 x a 0 ` x a` Ž . Ž . Ž . Ž . We remark that, if u t is a nonnegative solution of 1l , 2 , then u t is w x concave on 0, 1 . Ž . Ž . Boundary value problems 1l , 2 describe many phenomena in the applied mathematical sciences, which can be found in the theory of nonlinear diffusion generated by nonlinear sources, in thermal ignition of U E-mail address: hendej2@mail.auburn.edu. † E-mail address: wangh@math.msu.edu.

Johnny Henderson | Haiyan Wang | J. Henderson | Haiyan Wang

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