Immobilization of convex bodies in $${\mathbb {R}}^n$$ R n

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...

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

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...

Infinitely many solutions for a class of $p$-biharmonic‎ ‎equation in $mathbb{R}^N$

‎Using variational arguments‎, ‎we prove the existence of infinitely‎ ‎many solutions to a class of $p$-biharmonic equation in‎ ‎$mathbb{R}^N$‎. ‎The existence of‎ ‎nontrivial‎ ‎solution is established under a new‎ ‎set of hypotheses on the potential $V(x)$ and the weight functions‎ ‎$h_1(x)‎, ‎h_2(x)$‎.