2023-03-24T03:57:49Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/697452022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116On the maximum value of ground states for the scalar field equation with double power nonlinearityKawano, Shinjiopen access410We evaluate the maximum value of the unique positive solution to < u + f(u) = 0 in Rn, im x|→∞ (x) = 0, here (u) = ¡ωu + up ¡ uq, ω > 0, q > p > 1. t is known that a positive solution to this problem exists if and only if (u) := u f(s)ds > 0 for some u > 0. Moreover, Ouyang and Shi in 1998 ound that the solution is unique. In the present paper we investigate the aximum value of the solution. The key idea is to examine the function efined from the nonlinearity, which arises from the well-known Pohozaev dentity.Department of Mathematics, Hokkaido University2009-02-12engdepartmental bulletin paperVoRhttps://doi.org/10.14943/84085http://hdl.handle.net/2115/6974510.14943/84085Hokkaido University Preprint Series in Mathematics93718https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69745/1/pre937.pdfapplication/pdf95.42 KB2009-02-12