Positive Solutions For a Schr\"odinger-Bopp-Podolsky system in $\mathbb R^{3}$

Existence of positive solutions for a Schrödinger-Poisson system with bounded potential and weighted functions in R3$\mathbb{R}^{3}$

where V (x), a(x) and b(x) are positive and bounded in R, K(x) ∈ L(R) ∪ L∞(R) and K(x) ≥  in R. We will prove the existence of a positive solution (u,φ) ∈ W ,(R) × D,(R) for λ ∈R and  < q <m < ∗, where ∗ =  is the critical exponent for the Sobolev embedding in dimension . The assumption ‘ < q <m < ’ implies that the nonlinear term f (x,u) = a(x)|u|m–u + λb(x)|u|q–u in (.)...

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 ‎$h_1(x)‎, ‎h_2(x)$‎.

Existence and multiplicity of positive solutions for a coupled system of perturbed nonlinear fractional differential equations

In this paper, we consider a coupled system of nonlinear fractional differential equations (FDEs), such that both equations have a particular perturbed terms. Using emph{Leray-Schauder} fixed point theorem, we investigate the existence and multiplicity of positive solutions for this system.

Smoke-Ring Solutions of Gierer-Meinhardt System in R3

Abstract. We consider the steady states of the Gierer–Meinhardt system on all of R: εΔa − a + a hq = 0, Δh − h + a hs = 0 with an additional restriction q = p − 1. In the limit ε → 0, we use formal asymptotics to construct a solution whose activator component a concentrates on a circle. Under the additional constraints p > 1, m > 0, and 1 < m− s < 3, we find that such a solution exists and is u...

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