Related papers: Existence results for double-phase problems via Mo…
We prove an abstract critical point theorem based on a cohomological index theory that produces pairs of nontrivial critical points with nontrivial higher critical groups. This theorem yields pairs of nontrivial solutions that are neither…
We study Morse theory on noncompact manifolds equipped with exhaustions by compact pieces, defining the Morse homology of a pair which consists of the manifold and related geometric/homotopy data. We construct a collection of Morse data…
We establish some existence results for a class of critical $N$-Laplacian problems in a bounded domain in ${\mathbb R}^N$. In the absence of a suitable direct sum decomposition, we use an abstract linking theorem based on the ${\mathbb…
Two-grid theory plays a fundamental role in the design and analysis of multigrid methods. This paper is devoted to a new convergence analysis of two-grid methods for singular and symmetric positive semidefinite systems. Specifically, we…
We classify global Lipschitz solutions to two-phase free boundary problems governed by concave fully nonlinear equations, as either two-plane solutions or solutions to a one-phase problem.
A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.
We investigate the existence of positive solutions to fractional equations presenting a double criticality: a multi-polar Hardy-type potential and a Sobolev critical nonlinearity. The nonlocal nature of the operator and the absence of…
We study relativistic Kepler problems in the plane. At first, using non-smooth critical point theory, we show that under a general time-periodic external force of gradient type there are two infinite families of T-periodic solutions,…
We discuss the analytical solution of the two-loop sunrise graph with arbitrary non-zero masses in two space-time dimensions. The analytical result is obtained by solving a second-order differential equation. The solution involves elliptic…
The paper deals with homogenization of a model problem describing an immiscible compressible two-phase flow in random statistically homogeneous porous media. We derive the effective (macroscopic) problem and prove the convergence of…
In this paper, we study black hole solutions in double field theory. In the first part, we introduce a solution-generating method and classify black hole solutions into three categories in standard double field theory. To solve the problem…
This article is a follow up of our submitted paper [11] in which a decomposition of the Richards equation along two soil layers was discussed. A decomposed problem was formulated and a decoupling and linearisation technique was presented to…
By using truncation technique, minimization method and Morse theory, we obtain three nontrivial solutions for a class of semilinear elliptic equations.
We study two effective theories for QCD at non-zero temperature and finite chemical potential, using local Polyakov loops as the degrees of freedom. The sign problem is solved by exactly mapping the partition function to a sum over flux and…
A local criterion of topological phase transitions is established based on the Morse theory: a topological phase transition occurs when the count of Morse critical points of the order function changes. The locations in space where this…
In this paper we consider quasilinear elliptic equations with double phase phenomena and a reaction term depending on the gradient. Under quite general assumptions on the convection term we prove the existence of a weak solution by applying…
This paper deals with existence of a nontrivial positive solution to systems of equations involving nontrivial nonhomogeneous terms and critical or subcritical nonlinearities. Via a minimization argument we prove existence of a positive…
We construct Morse homology groups associated with any regular function on a smooth complex algebraic variety, allowing singular and non-compact critical loci. These groups are generated by critical points of a certain large pertubation of…
At low temperatures ultrasoft particle systems develop interesting phases via the self-assembly of particle clusters. In this study we develop a general zero-temperature analysis fully characterizing the ground state of such models in two…
Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge-B\"acklund transformation, underlying symmetries among superficially…