相关论文: Existence of Strong and Nontrivial Solutions to St…

In this paper we use variational methods to establish the existence of solutions for a class of nonlinear elliptic problems involving a combined convolution-type and Hardy nonlinearity with subcritical and critical growth.

In this article we find the equivalent conditions to assure the existence and uniqueness of positive solutions to semilinear elliptic equations wih double power nonlinearities. As a bonus, we give a simpler proof of our former result that…

Based on the theory of invariant sets of descending flow, we give a new proof of the existence of three nontrivial solutions and some remarks on it.

We establish the global existence of a class of strongly coupled parabolic systems. The necessary apriori estimates will be obtained via our new approach to the regularity theory of parabolic scalar equations with integrable data and new…

We discuss the existence and non-existence of non-negative weak solutions for second order nonlocal elliptic systems subject to functional boundary conditions. Our approach is based on classical fixed point index theory combined with some…

For elliptic systems defined on Riemann surfaces, Liouville and Toda systems represent two well-known classes exhibiting drastically different solution structures. Over the years, existence results for these systems have highlighted…

We investigate classical solutions of nonlinear elliptic equations with two classes of dynamical boundary conditions, of reactive and reactive-diffusive type. In the latter case it is shown that well-posedness is to a large extent…

We consider positive singular solutions to semilinear elliptic problems with possibly singular nonlinearity. We deduce symmetry and monotonicity properties of the solutions via the moving plane procedure.

This paper considers a class of noncoercive nonlinear elliptic problems with coefficients defined in Marcinkiewicz and Lorentz spaces. We prove the existence of a solution for the corresponding Dirichlet problem and investigate the higher…

We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…

We prove the existence of non-trivial solutions to a system of coupled, nonlinear, Schroedinger equations with general nonlinearity.

A system of quasilinear elliptic equations on an unbounded domain is considered. The existence of a sequence of radially symmetric weak solutions is proved via variational methods.

In this paper, we investigate the existence of nontrivial weak solutions to a class of elliptic equations ($\mathscr{P}$) involving a general nonlocal integrodifferential operator $\mathscr{L}_{\mathcal{A}K}$, two real parameters, and two…

This work gathers new results concerning the semi-geostrophic equations: existence and stability of measure valued solutions, existence and uniqueness of solutions under certain continuity conditions for the density, convergence to the…

We establish the existence of multiple solutions for singular quasilinear elliptic problems with a precise sign information: two opposite constant sign solutions and a nodal solution. The approach combines sub-supersolutions method and…

Three classes of higher-order nonlinear parabolic hyperbolic, and nonlinear dispersion equations are shown to admit exact blow-up or compacton solutions, which are induced by elliptic equations with non-Lipschitz nonlinearities. Variational…

We study systems of stochastic differential equations describing positions x_1,x_2,...,x_p of p ordered particles, with inter-particles repulsions of the form H_{ij}(x_i,x_j)/(x_i-x_j). We show the existence of strong and pathwise unique…

Existence, regularity and location of solutions to quasilinear singular elliptic systems with general gradient dependence are established developing a method of sub-supersolution. The abstract theorems involving sub-supersolutions are…

We develop a unified framework for a broad class of nonlocal elliptic problems, encompassing a wide spectrum of nonlocal terms, including the classical Kirchhoff and Carrier-type equations as particular cases, and nonlinearities having…

We study the existence of fully nontrivial solutions to the system $$-\Delta u_i+ \lambda_iu_i = \sum\limits_{j=1}^\ell \beta_{ij}|u_j|^p|u_i|^{p-2}u_i\ \hbox{in}\ \Omega, \qquad i=1,\ldots,\ell,$$ in a bounded or unbounded domain $\Omega$…