相关论文: Critical Elliptic Systems in Potential Form

An approximate analytical expression for "capacitance" of MWPC configurations circulates in the literature since decades and is copied over and over again. In this paper we will try to show that this formula corresponds to a physical…

General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hypergeometric terms leading to multidimensional integrals on…

We prove doubling inequalities for solutions of elliptic systems with an iterated Laplacian as diagonal principal part and for solutions of the Lame' system of isotropic linearized elasticity. These inequalities depend on global properties…

We investigate the existence of multiple periodic solutions to the anisotropic discrete system. We apply the linking method and a new three critical point theorem which we provide.

A $p$-Laplacian elliptic problem in the presence of both strongly singular and $(p-1)$-superlinear nonlinearities is considered. We employ bifurcation theory, approximation techniques and sub-supersolution method to establish the existence…

In this paper we prove classification results for solutions to subcritical and critical semilinear elliptic equations with a nonnegative potential on noncompact manifolds with nonnegative Ricci curvature. We show in the subcritical case…

We investigate integrable 2-dimensional Hamiltonian systems with scalar and vector potentials, admitting second invariants which are linear or quadratic in the momenta. In the case of a linear second invariant, we provide some examples of…

We show that the use of generalized multivariable forms of Hermite polynomials provide an useful tool for the evaluation of families of elliptic type integrals often encountered in electrostatic and electrodynamics

We establish some upper and lower bounds of the rational topological complexity for certain classes of elliptic spaces. Our techniques permit us in particular to show that the rational topological complexity coincides with the dimension of…

We provide new results on the existence, non-existence and multiplicity of non-negative radial solutions for semilinear elliptic systems with Neumann boundary conditions on an annulus. Our approach is topological and relies on the classical…

In this paper we are concerned with the number of nonnegative solutions of the elliptic system $$ {array}{ll} -\Delta u = Q_u(u,v) + 1/2{2^*} H_u(u,v),& {in} \Omega,\vdois\ -\Delta v = Q_v(u,v) + 1/{2^*} H_v(u,v),& {in} \Omega,\vdois\…

We study a nonlinear system made up of an elliptic equation of blended singular/degenerate type and Poisson's equation with a lowly integrable source. We prove the existence of a weak solution in any space dimension and, chiefly, derive an…

We study a nonlinear elliptic problem defined in a bounded domain involving fractional powers of the Laplacian operator together with a concave-convex term. We characterize completely the range of parameters for which solutions of the…

Using variational methods we prove some results about existence and multiplicity of positive bound states of to the following Schr\"odinger-Poisson system: $$ \left\{ \begin{array}{l} \vspace{2mm} -\Delta u+V(x)u+K(x)\phi(x)u=u^5 -\Delta…

The problem of separation of variables in some coordinate systems obtained with the use of $L$-transformations is studied. Potentials are shown that allow separation of regular variables in a perturbed two-body problem. The potential…

We are concerned with the well-posedness of linear elliptic systems posed on $\mathbb{R}^d$. The concrete problem of interest, for which we require this theory, arises from the linearization of the equations of anisotropic finite…

Through Morrey's spaces (plus Zorko's spaces) and their potentials/capacities as well as Hausdorff contents/dimensions, this paper estimates the singular sets of nonlinear elliptic systems of the even-ordered Meyers-Elcrat type and a class…

We consider the linear elliptic systems or equations in divergence form with periodically oscillating coefficients. We prove the large-scale boundary Lipschitz estimate for the weak solutions in domains satisfying the so-called…

We define an abstract nonlinear elliptic system, admitting a variational structure, and including the vortex equations for some Maxwell-Chern-Simons gauge theories as special cases. We analyze the asymptotic behavior of its solutions, and…

In this paper, several nonlinear elliptic systems are investigated on graphs. One type of the sobolev embedding theorem and a new version of the strong maximum principle are established. Then, by using the variational method, the existence…