کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
839708 | 1470487 | 2015 | 21 صفحه PDF | دانلود رایگان |
Let XX be a real reflexive locally uniformly convex Banach space with locally uniformly convex dual space X∗X∗. Let T:X⊇D(T)→2X∗T:X⊇D(T)→2X∗ be maximal monotone and S:X→2X∗S:X→2X∗ be bounded pseudomonotone. Let pp be a nonnegative integer. Assume, further, that there exist nonnegative constants ai(i=1,2,…,p) such that 〈v∗+w∗,x〉≥−∑i=1pai‖x‖i−α(‖x‖)‖x‖p+2 for all x∈D(T)x∈D(T) with sufficiently large ‖x‖‖x‖, v∗∈Txv∗∈Tx and w∗∈Sxw∗∈Sx, where α:[0,∞)→[0,∞)α:[0,∞)→[0,∞) such that α(t)→0α(t)→0 as t→∞t→∞. New surjectivity results are given for the operator T+ST+S along with weakly coercive type hypothesis on T+ST+S. The results are new and improve the corresponding theory for coercive operators of monotone type. The theory developed herein can be suitably applied in the study of partial differential equations, variational and hemi-variational inequality problems in appropriate Sobolev spaces. To demonstrate the applicability of the theory, an example of time periodic parabolic partial differential equation, which models nonmonotone semipermeability problem, is provided.
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 113, January 2015, Pages 209–229