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In this paper we establish existence and multiplicity of solutions for an elliptic system which has strong resonance at first eigenvalue. To describe the resonance, we use an eigenvalue problem with indefinite weight. In all results we use Variational Methods.
It is well known that a single nonlinear fractional Schrodinger equation with a potential $V(x)$ and a small parameter $varepsilon $ may have a positive solution that is concentrated at the nondegenerate minimum point of $V(x)$. In this paper, we can
A well-known diffuse interface model for incompressible isothermal mixtures of two immiscible fluids consists of the Navier-Stokes system coupled with a convective Cahn-Hilliard equation. In some recent contributions the standard Cahn-Hilliard equati
We study positive solutions to the fractional Lane-Emden system begin{equation*} tag{S}label{S} left{ begin{aligned} (-Delta)^s u &= v^p+mu quad &&text{in } Omega (-Delta)^s v &= u^q+ u quad &&text{in } Omega u = v &= 0 quad &&text{in } Omega^c={mat
In this paper, we study a class of generalized extensible beam equations with a superlinear nonlinearity begin{equation*} left{ begin{array}{ll} Delta ^{2}u-Mleft( Vert abla uVert _{L^{2}}^{2}right) Delta u+lambda V(x) u=f( x,u) & text{ in }mathbb{R
This article is concerned with the existence and the long time behavior of weak solutions to certain coupled systems of fourth-order degenerate parabolic equations of gradient flow type. The underlying metric is a Wasserstein-like transportation dist