Related papers: Two solutions to Kazdan-Warner's problem on surfac…

In this paper, we investigate a Kazdan-Warner problem on compact K\"ahler surfaces, which corresponds to prescribing sign-changing Chern scalar curvatures, and establish a Chen-Li type existence theorem on compact K\"ahler surfaces when the…

In this note, we prove an existence result for generalized Kazdan-Warner equations on compact Riemannian manifolds by using the flow approach or the upper and lower solution method. In addition, we give a prior estimate for this type…

In this paper, we study the following Kazdan-Warner equation with sign-changing prescribed function $h$ \begin{align*} -\Delta u=8\pi\left(\frac{he^{u}}{\int_{\Sigma}he^{u}}-1\right) \end{align*} on a closed Riemann surface whose area is…

Let $G=(V,E)$ be a finite connected graph, and let $\kappa: V\rightarrow \mathbb{R}$ be a function such that $\int_V\kappa d\mu<0$. We consider the following Kazdan-Warner equation on $G$:\[\Delta u+\kappa-K_\lambda e^{2u}=0,\] where…

After R.~Schoen completed the solution to the Yamabe problem, compact manifolds could be categorized into three classes, depending on whether they admit a metric with positive, non-negative, or only negative scalar curvature. Here we follow…

In this paper we address two boundary cases of the classical Kazdan-Warner problem. More precisely, we consider the problem of prescribing the Gaussian and boundary geodesic curvature on a disk of R^2, and the scalar and mean curvature on a…

We consider the case with boundary of the classical Kazdan-Warner problem in dimension greater or equal than three, i.e. the prescription of scalar and boundary mean curvatures via conformal deformations of the metric. We deal in particular…

We are interested in looking for two nontrivial solutions for a class of nonhomogeneous quasilinear elliptic system with sign-changing weight functions and concave-convex nonlinearities on the bounded domain. This kind of quasilinear…

In this paper we analyse some possibilities of finding positive solutions for second order boundary value problems with Dirichlet and periodic boundary conditions, for which the correspondent Green's functions change sign. The obtained…

We solve the modified Kazdan-Warner problem of finding metrics with prescribed scalar curvature and unit total volume.

We solve the Cauchy problem of the Ward model in light-cone coordinates using the inverse spectral (scattering) method. In particular we show that the solution can be constructed by solving a $2\times 2$ local matrix Riemann-Hilbert problem…

In this paper we are concerned with some $p$-Kirchhoff type problems involving sign-changing weight functions. We prove the existence of multiple positive solutions of the problem via the Nehari manifold approach.

In this paper, we are concerned with the sign-changing solutions of variational inequality problems. In order to give the existence results of the sign-changing solutions for variational inequality problems, we first construct a suitable…

On a closed Riemannian manifold $(M^n ,g)$, we consider the Yamabe-type equation $-\Delta_g u + \lambda u = \lambda |u|^{q-1}u$, where $\lambda \in \mathbb{R}_{+}$ and $q>1$. We assume that $M$ admits a proper isoparametric function $f$…

We study a $p$-Laplacian equation involving a parameter $\lambda$ and a concave-convex nonlinearity containing a weight which can change sign. By using the Nehari manifold and the fibering method, we show the existence of two positive…

We prove an existence theorem for positive solutions to Lichnerowicz-type equations on complete manifolds with boundary and nonlinear Neumann conditions. This kind of nonlinear problems arise quite naturally in the study of solutions for…

In this paper we study quasilinear elliptic equations driven by the so-called double phase operator and with a nonlinear boundary condition. Due to the lack of regularity, we prove the existence of multiple solutions by applying the Nehari…

A result of existence of a nonnegative and a nontrivial solution is proved via critical point theorems for non smooth functionals. The equation considered presents a convex part and a nonlinearity which changes sign.

We study the 2+1 dimensional XY model at nonzero chemical potential $\mu$ on deformed integration manifolds, with the aim of alleviating its sign problem. We investigate several proposals for the deformations, and considerably improve on…

This paper is concerned with the existence of sign-changing solutions to non local Kirchhoff type problems of the form \begin{equation}\label{s}\tag{S} -\Big(a+b\int_\Omega|\nabla u|^2dx\Big)\Delta u=f(x,u)\, \text{ in }\Omega,\quad\quad…