This paper is dedicated to studying nonstationary homoclinic solutions with the least energy for a class of fractional reaction-diffusion system \begin{document}$ \begin{eqnarray*} \label{1.1} \left\{\begin{array}{lll} \partial_t u+ (-\Delta)^s u+V(x)u+W(x)v = H_v(t, x, u, v), \\ - v + v+V(x)v+W(x)u H_u(t, |u(t, x)|+|v(t, x)|\rightarrow 0, \ \text{as}\ |t|+|x|\rightarrow \infty, \end{array} \ri...

<p style='text-indent:20px;'>This paper study nonstationary homoclinic-type solutions for a fractional reaction-diffusion system with asymptotically linear and local super nonlinearity. The resulting problem engages two major difficulties: one is that the associated functional strongly indefinite, second lies in verifying link geometry showing boundedness of Cerami sequences when nonlinea...

In this paper, we study the following nonlinear Dirac–Bopp–Podolsky system −i∑k=13αk∂ku+[V(x)+q]βu+wu−ϕu=f(x,u),in R3,−△ϕ+a2△2ϕ=4π|u|2,in R3,where a,q>0,w∈R, V(x) is a potential function, and f(x,u) interaction term (nonlinearity). First, give physical motivation for new kind of system. Second, under suitable assumptions on f V, by means minimax techniques involving Cerami sequences, prove exis...

The aim of this paper is investigating the existence one or more weak solutions coupled quasilinear elliptic system gradient type \[ (P)\qquad \left\{ \begin{array}{ll} - {\rm div} (A(x, u)\vert\nabla u\vert^{p_1 -2} \nabla u) + \frac{1}{p_1}A_u (x, u\vert^{p_1} = G_u(x, u, v) &\hbox{ in $\Omega$,}\\[5pt] (B(x, v)\vert\nabla v\vert^{p_2 +\frac{1}{p_2}B_v(x, v\vert^{p_2} G_v\left(x, v\right) u v...

The term FKPM (fragments per kilobase of transcript per million fragments sequenced) is incorrect throughout. The correct description should be FPKM (Fragments Per Kilobase Of Exon Per Million Fragments Mapped). The following references are omitted in the article: Two references are omitted from the second sentence of the second paragraph in the Introduction. The sentence should read: In recent...

Let us consider the quasilinear problem [Formula: see text] where is a bounded domain in with smooth boundary, text], parameter and continuous function having subcritical growth. We prove that there exists such that, for every has at least solutions, possibly counted their multiplicities, Poincaré polynomial of text]. Using Morse techniques, we furnish an interpretation multiplicity solution, t...

where Ω is a bounded and smooth subset of Rn , n 1, m > 0 and p 1. Problem (1.1)–(1.3) (see Galaktionov, 1981; Samarskii et al., 1995) describes the propagation of thermal perturbations in a medium with a nonlinear heat conduction coefficient and a heat source depending on the temperature when u0 0. Local existence for the solutions of (1.1)–(1.3) has been proved when m > 1 (the so-called slow ...