Related papers: The solution of Hutn\'ik's open problem
We prove the existence of positive solutions for a class of semipositone problem with singular Trudinger-Moser nonlinearities. The proof is based on compactness and regularity arguments.
In this paper we classify positive solutions to the critical semilinear elliptic equation in $\mathbb{H}^n$. We prove that they are the Jerison-Lee's bubbles, provided $n=1$ or $n\geq 2$ and a suitable control at infinity holds. The proofs…
Version 2: Corrected Section 3.3: instead of lexicographical normal forms we now use a normal form due to V. Diekert and A. Muscholl. Consequent changes made and some misprints corrected. Using an analogue of Makanin-Razborov diagrams, we…
In this paper we obtain a Liouville type theorem to the semilinear subcritical elliptic equation on H-type groups. The semilinear subcritical elliptic equation studied in this paper is a generalization of a classical semilinear subcritical…
In a recent article by the authors [15] it was shown that wide classes of semilinear elliptic equations with exponential type nonlinearities admit singular radial solutions $U$ on the punctured disc in $\mathbb R^2$ which are also…
We show that fuzzy spheres are solutions of ${\it Lorentzian}$ IKKT matrix models. The fuzzy sphere solutions serve as toy models of closed noncommutative cosmologies where big bang/crunch singularities appear only after taking the…
In this paper, using the technical tools in \cite{TW5}, we solve the complex Hessian equation on closed Hermitian manifolds, which generalizes the the K\"ahler case results in \cite{HMW} and \cite{DK}.
In this paper, we use a new method to obtain the necessary and sufficient condition guaranteeing the validity of the Minkowski-H\"{o}lder type inequality for the generalized upper Sugeno integral in the case of functions belonging to a…
The aim of this paper is to deal with the $k$-Hessian counterpart of the Laplace equation involving a nonlinearity studied by Matukuma. Namely, our model is the problem \begin{equation*} (1)\;\;\;\begin{cases} S_k(D^2u)= \lambda…
In this paper, it is proved that, for the truth value algebra of interval-valued fuzzy sets, the distributive laws do not imply the monotonicity condition for the set inclusion operation. Then, a lattice-ordered $t_{r}$-norm, which is not…
We are concerned with a class of nonconvex and nonsmooth composite optimization problems, comprising a twice differentiable function and a prox-regular function. We establish a sufficient condition for the proximal mapping of a prox-regular…
We establish a necessary and sufficient condition for solving a general class of fully nonlinear elliptic equations on closed Riemannian or hermitian manifolds, including both hessian and hessian quotient equations. It settles an open…
The existence problem is solved, and global pointwise estimates of solutions are obtained for quasilinear and Hessian equations of Lane-Emden type, including the following two model problems: $ -\Delta_p u = u^q + \mu$ and $F_k[-u] = u^q +…
We prove analogs of the Bezout and the Bernstein-Kushnirenko-Khovanskii theorems for systems of algebraic differential conditions over differentially closed fields. Namely, given a system of algebraic conditions on the first $l$ derivatives…
This study focuses on the Cauchy problem associated with the two-component peakon system featuring a cubic nonlinearity, constrained to the class $(m,n)\in C^{k}(\mathbb{R}) \cap W^{k,1}(\mathbb{R})$ with $k\in\mathbb{N}\cup\{0\}$.This…
This paper concerns the existence of a solution for the following class of semipositone quasilinear problems \begin{equation*} \left \{ \begin{array}{rclcl} -\Delta_p u = h(x)(f(u)-a),\ & u > 0 & \mbox{in} & \mathbb{R}^N, \end{array}…
We introduce a series of $\Z_2^n$-graded quasialgebras $\bbP_n(m)$ which generalizes Clifford algebras, higher octonions, and higher Cayley algebras. The constructed series of algebras and their minor perturbations are applied to contribute…
The exact general solution to the Einstein equations in a homogeneous Universe with a full causal viscous fluid source for the bulk viscosity index $m=1/2$ is found. We have investigated the asymptotic stability of Friedmann and de Sitter…
Since K\H{o}v\'ari, S\'os, and Tur\'an proved upper bounds for the Zarankiewicz problem in 1954, much work has been undertaken to improve these bounds, and some have done so by restricting to particular classes of graphs. In 2017, Fox,…
This paper answers the conjecture of Adimurthi and Struwe that the semilinear Trudinger-Moser functional (as well as functionals with more general critical nonlinearities) satisfies the Palais-Smale condition at all levels except n/2 for…