相关论文: Existence results for non-coercive variational pro…
In this work, we consider a boundary value problem for nonlinear triharmonic equation. Due to the reduction of nonlinear boundary value problems to operator equation for nonlinear terms we establish the existence, uniqueness and positivity…
In this note we develop a framework which allows to prove an existence result for non-linear evolution problems involving time-dependent, pseudo-monotone operators. This abstract existence result is applicable to a large class of concrete…
In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role…
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…
The aim of this article is to present an elementary proof of a global existence result for nonlinear wave equations satifying the null condition in an exterior domain. The novelty of our proof is to avoid completely the scaling operator…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
We study existence and Lorentz regularity of distributional solutions to elliptic equations with either a convection or a drift first order term. The presence of such a term makes the problem not coercive. The main tools are pointwise…
In the presence of a certain class of functions we show that there exists a smooth solution to Navier-Stokes equation. This solution entertains the property of being nonconvective. We introduce a definition for any possible solution to the…
We study a class of nonlinear eigenvalue problems which involves a convolution operator as well as a superlinear nonlinearity. Our variational existence proof is based on constrained optimization and provides a one-parameter family of…
We establish the existence of loop type subcontinua of nonnegative solutions for a class of concave-convex type elliptic equations with indefinite weights, under Dirichlet and Neumann boundary conditions. Our approach depends on local and…
We establish a positivity property for a class of semilinear elliptic problems involving indefinite sublinear nonlinearities. Namely, we show that any nontrivial nonnegative solution is positive for a class of problems the strong maximum…
We provide a unified framework for a systematic analysis of the existence of solutions to general nonconvex problems, relying on asymptotic and retractive cones for functions and sets. Using this framework we develop new necessary and…
We give a variational proof of the existence and uniqueness of a convex cap with the given upper boundary. The proof uses the concavity of the total scalar curvature functional on the space of generalized convex caps. As a byproduct, we…
The qualitative analysis of the initial value problem P related to a non linear third order parabolic equation typical of diffusive models is discussed. Some basic properties of the the fundamental solution of a related linear operator are…
This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…
We establish the existence, uniqueness, and $W^{1,2,p}$-regularity of solutions to fully-nonlinear, parabolic obstacle problems when the obstacle is the pointwise supremum of functions in $W^{1,2,p}$ and the nonlinear operator is required…
We present a numerical method for the solution of Newton's problem of least resistance in the class of convex functions using a convex hull approach. We observe that the numerically computed solutions possess some symmetry. Further, their…
Differential inclusions with compact, upper semi-continuous, not necessarily convex right-hand sides in R^n are studied. Under a weakened monotonicity-type condition the existence of solutions is proved.
Nonconvex functionals with spherical symmetry are studied. Existence of one and radial symmetry of all global minimizers is shown with an approach based on convex relaxation.
We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set, which is characterized by a constraint on the absolute value of the gradient that depends…