$C^1$-homogeneous compacta in $\mathbb {R}^n$ are $C^1$-submanifolds of $\mathbb {R}^n$

Transcendental submanifolds of Rn

In this paper we show how the restriction of the complex algebraic cycles to real part of a complex algebraic set îs related to the real algebraic cycles of the real part As a corollary we give examples of smooth submanifolds of a Euchdean space which can not be isotoped to real parts of complex nonsingular subvaneties in the corresponding projective space Algebraic numbers are dense in R. The ...

Existence of a ground state solution for a class of singular elliptic problem in RN$\mathbb{R}^{N}$

when p = , |f (x,u)| ≤ c(|u|+ |u|q–),  < q≤ ∗ = N N– ,N ≥ , for the corresponding results onemay refer to Brézis [], Brézis and Nirenberg [], Bartsch andWillem [] and Capozzi, Fortunato and Palmieri []. Garcia and Alonso [] generalized Brézis, Nirenberg’s existence and nonexistence results to p-Laplace equation. Moreover, let us consider the following semilinear Schrödinger equation:

Existence of nontrivial solutions for a class of biharmonic equations with singular potential in RN$\mathbb{R}^{N}$

*Correspondence: [email protected] School of Mathematics and Physics, University of South China, Hengyang, P.R. China Abstract In this paper, we study a class of biharmonic equations with a singular potential inRN . Under appropriate assumptions on the nonlinearity, we establish some existence results via the Morse theory and variational methods. We significantly extend and complement some re...

Positive solutions for coupled Schrödinger system with critical exponent in RN$\mathbb{R}^{N}$ (N≥5$N\geq5$)

Infinitely many solutions for p-biharmonic equation with general potential and concave-convex nonlinearity in RN$\mathbb{R}^{N}$

In this paper, we study the existence of multiple solutions to a class of p-biharmonic elliptic equations, pu – pu + V(x)|u|p–2u = λh1(x)|u|m–2u + h2(x)|u|q–2u, x ∈RN , where 1 0. By variational methods, we obtain the existence of infini...