Related papers: An existence result for non-coercive non-convex pr…

We establish the necessary and sufficient conditions for constructing gradient Einstein-type warped metrics. One of these conditions leads us to a general Lichnerowicz equation with analytic and geometric coefficients for this class of…

We study qualitative properties of positive solutions of noncooperative, possibly nonvariational, elliptic systems. We obtain new classification and Liouville type theorems in the whole Euclidean space, as well as in half-spaces, and deduce…

We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no…

We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of…

We present an existence theorem for a large class of nonlinearly elastic shells with low regularity in the framework of a two-dimensional theory involving the mean and Gaussian curvatures. We restrict our discussion to hyperelastic…

We prove an existence theorem for the Cauchy problem on a characteristic cone for the vacuum Einstein equations.

This work is concerned with Hamilton-Jacobi equations of evolution type posed in domains and supplemented with boundary conditions. Hamiltonians are coercive but are neither convex nor quasiconvex. We analyse boundary conditions when…

We consider a nonlocal differential equation of Kirchhoff type with a convolution coefficient involving variable growth. The novelty of our work lies in allowing a variable exponent in the nonlocal term. By relating the variable growth…

We consider parabolic problems with non-Lipschitz nonlinearity in the different scales of Banach spaces and prove local-in-time existence theorem. New class of parabolic equations that have analytic solutions is obtained.

We adapt a technique of nonsmooth critical point theory developed by Degiovanni-Zani for a semilinear problem involving the Laplacian to the the case of the $p$-Laplacian. We suppose only coercivity conditions on the potential and impose no…

In this paper, we study the existence of nonnegative solutions for a class of multivalued $(p,N)$-Laplace problems having discontinuous nonlinearity with critical exponential growth in $\mathbb{R}^N$. To demonstrate the existence results,…

We present several Liouville type results for the $p$-Laplacian in $\R^N$. Suppose that $h$ is a nonnegative regular function such that $$ h(x) = a|x|^\gamma\ {\rm for}\ |x|\ {\rm large},\ a>0\ {\rm and}\ \gamma> -p. $$ We obtain the…

In this paper we investigate the bound state problem of nonrelativistic quantum particles on a conical surface. This kind of surface appears as a topological defect in ordinary semiconductors as well as in graphene sheets. Specifically, we…

This paper concerns a nonlinear elliptic equation involving a critical Sobolev growth and a lower-order term. Under a Lions's condition, we prove the existence of at least one positive solution. Our approach consists in constructing a…

We consider the motion of incompressible viscous non-homogeneous fluid described by the Navier-Stokes equations in a bounded cylinder under boundary slip conditions. Assume that the third co-ordinate axis is the axis of the cylinder.…

In this paper, by using a characterization of functions having fractional derivative, we propose a rigorous fractional Lyapunov function candidate method to analyze stability of fractional-order nonlinear systems. First, we prove an…

Variational problems under uniform quasiconvex constraints on the gradient are studied. In particular, existence of solutions to such problems is proved as well as existence of lagrange multipliers associated to the uniform constraint. They…

We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear difference equations assuming a very general form of dichotomic behavior for the linear equation. The results obtained…

In this paper we prove a Liouville type theorem for the stationary equations of a non-Newtonian fluid in $\mathbb{R}^3$ with the viscous part of the stress tensor $\mathbf{A}_p(u) = \mathrm{div} ( | \mathbf{D}(u) |^{p-2} \mathbf{D}(u) )$,…

We deal with existence and non-existence of non-negative entire solutions that blow-up at infinity for a quasilinear problem depending on a non-negative real parameter. Our main objectives in this paper are to provide far more general…