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The existence of an unbounded sequence of solutions to a conformally invariant elliptic equation having nonlocal critical-power nonlinearity is established. The primary obstacle to establishing existence of solutions is the failure of…
In this paper, we prove new existence and multiplicity results for critical points of lower semicontinuous functionals in Banach spaces, complementing the nonsmooth critical point theory set forth by Szulkin and avoiding the need of the…
In this paper we establish, using variational methods combined with the Moser-Trudinger inequality, existence and multiplicity of weak solutions for a class of critical fractional elliptic equations with exponential growth without a…
In this paper, we study a class of singular double phase problems defined on Minkowski spaces in terms of Finsler manifolds and with right-hand sides that allow a certain type of critical growth for such problems. Under very general…
In this paper we study a nonlocal critical growth elliptic problem driven by the fractional Laplacian in presence of jumping nonlinearities. In the main results of the paper we prove the existence of a nontrivial solution for the problem…
This survey on stationary and evolutionary problems with gradient constraints is based on developments of monotonicity and compactness methods applied to large classes of scalar and vectorial solutions to variational and quasi-variational…
We prove the existence of ground state positive solutions for a class of semipositone $p$-Laplacian problems with a critical growth reaction term. The proofs are established by obtaining crucial uniform $C^{1,\alpha}$ a priori estimates and…
This paper addresses a class of elliptic problems involving the superposition of nonlinear fractional operators with the critical Sobolev exponent in the sublinear regimes. We establish the existence of infinitely many nontrivial weak…
This paper studies the asymptotic convergence properties of the primal-dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by…
We prove that ancient non-negative solutions to a fully anisotropic prototype evolution equation are constant if they satisfy a condition of finite speed of propagation and if they are both one-sided bounded, and bounded in space at a…
We study the existence and multiplicity of positive solutions for a nonlinear fourth-order two-point boundary value problem. The approach is based on critical point theorems in conical shells, Krasnoselskii's compression-expansion theorem,…
We obtain nontrivial solutions for two types of critical $p$-Laplacian problems with asymmetric nonlinearities in a smooth bounded domain in ${\mathbb R}^N,\, N \ge 2$. For $p < N$, we consider an asymmetric problem involving the critical…
In this paper, we study a second-order, nonlinear evolution equation with damping arising in elastodynamics. The nonlinear term is monotone and possesses a convex potential but exhibits anisotropic and nonpolynomial growth. The appropriate…
We deal with boundary value problems for second-order nonlinear elliptic equations in divergence form, which emerge as Euler-Lagrange equations of integral functionals of the Calculus of Variations built upon possibly anisotropic norms of…
We give existence and regularity results for solutions of some nonlinear elliptic problems. The equations we deal with are modeled on a problem which involves in its principal part an anisotropic operator, a Hardy-type potential, and a…
We prove a Liouville type result for bounded, entire solutions to a class of variational semilinear elliptic systems, based on the growth of their potential energy over balls with growing radius. Important special cases to which our result…
This survey reviews variational and iterative methods for reconstructing non-negative solutions of ill-posed problems in infinite-dimensional spaces. We focus on two classes of methods: variational methods based on entropy-minimization or…
We shall prove a multiplicity result for semilinear elliptic problems with a super-critical nonlinearity of the form, \begin{equation}\label{con-c} \left \{ \begin{array}{ll} -\Delta u =|u|^{p-2} u+\mu |u|^{q-2}u, & x \in \Omega\\ u=0, & x…
We use extensive Monte Carlo transfer matrix calculations on infinite strips of widths $L$ up to 30 lattice spacing and a finite-size scaling analysis to obtain critical exponents and conformal anomaly number $c$ for the two-dimensional…
In this paper we study the existence of radially symmetric solitary waves in R^N for the nonlinear Klein-Gordon equations coupled with the Maxwell's equations when the nonlinearity exhibits critical growth. The main feature of this kind of…