Existence of Nontrivial Solutions for Generalized Quasilinear Schrödinger Equations with Critical Growth by Quanqing Li, Kaimin Teng, Xian Wu

“…We study the following generalized quasilinear Schrödinger equations with critical growth -divg2u∇u+gug′u∇u|2+Vxu=λfx,u+guGu|2⁎-2Gu,x∈RN, where λ>0, N≥3, g(s):R→R+ is a C1 even function, g(0)=1, and g′(s)≥0 for all s≥0, where G(u)≔∫0ug(t)dt. …”
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Ramanujan sums via generalized Möbius functions and applications by Vichian Laohakosol, Pattira Ruengsinsub, Nittiya Pabhapote

“…The first shows that the unique representation of even functions with respect to GRSs is possible. The second is a derivation of the mean value of a GRS. …”
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Nonlinear eigenvalue problems in Sobolev spaces with variable exponent by Teodora-Liliana Dinu

“…Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with a ℤ2-symmetric version for even functionals of the Mountain Pass Lemma and some adequate variational methods.…”
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