相关论文: Entire solutions to equations of minimal surface t…

We present a variational framework for studying the existence and regularity of solutions to elliptic free boundary problems that do not necessarily minimize energy. As applications, we obtain mountain pass solutions of critical and…

In this paper, we consider fully nonlinear equations of Krylov type on Riemannian manifolds with negative curvature which naturally arise in conformal geometry. Moreover, we prove the a priori estimates for solutions to these equations and…

Comparison results for solutions to the Dirichlet problems for a class of nonlinear, anisotropic parabolic equations are established. These results are obtained through a semi-discretization method in time after providing estimates for…

In this paper, we study totally real minimal surfaces in the quaternionic projective space $\mathbb{H}P^n$. We prove that the linearly full totally real flat minimal surfaces of isotropy order $n$ in $\mathbb{H}P^n$ are two surfaces in…

We prove, by topological methods, new results on the existence of nonzero positive weak solutions for a class of multi-parameter second order elliptic systems subject to functional boundary conditions. The setting is fairly general and…

We study fully nonlinear elliptic equations on Hermitian manifolds through blow-up argument and partial uniform ellipticity. We apply our results to draw geometric conclusions on finding conformal Hermitian metrics with prescribed…

We obtain a comparison result for solutions to nonlinear fully anisotropic elliptic problems by means of anisotropic symmetrization. As consequence we deduce a priori estimates for norms of the relevant solutions.

We prove the existence of ground state solutions for a class of nonlinear elliptic equations, arising in the production of standing wave solutions to an associated family of nonlinear Schr\"odinger equations. We examine two constrained…

We study the solvability of a class of fully nonlinear equations on the flat torus. The equations arise in the study of some Calabi-Yau type problems in torus bundles.

The main goal is to establish necessary and sufficient conditions under which the fractional semilinear elliptic equation $\Delta^{\frac{\alpha}{2}} u=\rho(x)\,\varphi(u)$ admits nonnegative nontrivial bounded solutions in the whole space…

In the framework of the nonsmooth critical point theory for lower semi-continuous functionals, we propose a direct variational approach to investigate the existence of infinitely many weak solutions for a class of semi-linear elliptic…

We study partial analyticity of solutions to elliptic systems and analyticity of level sets of solutions to nonlinear elliptic systems. We consider several applications, including analyticity of flow lines for bounded stationary solutions…

We give a complete topological classification of minimal surfaces in Euclidian three-space.

In this paper we prove existence of radial solutions for the nonlinear elliptic problem \[ -\mathrm{div}(A(|x|)\nabla u)+V(|x|)u=K(|x|)f(u) \quad \text{in }\mathbb{R}^{N}, \] \noindent with suitable hypotheses on the radial potentials…

The aim of this paper is investigating the existence of solutions of some semilinear elliptic problems on open bounded domains when the nonlinearity is subcritical and asymptotically linear at infinity and there is a perturbation term which…

We establish existence and qualitative properties of saddle-shaped solutions of the elliptic fractional equation $(-\Delta)^{1/2}u=f(u)$ in all the space $\re^{2m}$, where $f$ is of bistable type. These solutions are odd with respect to the…

We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.

The paper deals with positive radial solutions to a nonlinear elliptic equation with singular and decaying potential, for which several existence and nonexistence results are known, resting upon suitable compatibility conditions between the…

We prove that entire bounded monotone solutions to a certain class of fully nonlinear equations in 2D are one-dimensional. Our result also gives a new (non-variational) proof of the well known De Giorgi's conjecture.

We study existence of nontrivial solutions to problem \begin{equation*} \left\lbrace \begin{array}{rcll} -\Delta u &=& \lambda u+f(u)&\text{ in }\Omega,\\ u&=&0&\text{ on }\partial \Omega, \end{array}\right. \end{equation*} where $\Omega…