Related papers: Notes on asymptotic behavior of radial solutions f…
The main purpose of this paper is to capture the asymptotic behavior for solutions to a class of nonlinear elliptic and parabolic equations with the anisotropic weights consisting of two power-type weights of different dimensions near the…
The paper is devoted to the study of asymptotic behavior of solutions for nonlocal elliptic problems in weighted spaces. We deal with the most difficult case where the support of nonlocal terms intersects with the boundary of a plane…
This paper completes and partially improves some of the results of [arXiv:0809.5002] about the asymptotic behavior of solutions of linear and nonlinear elliptic equations with singular coefficients via an Almgren type monotonicity formula
We establish quantitative asymptotic behavior of positive solutions of a family of nonlinear elliptic equations on the half cylinder near the end. This unifies the study of isolated singularities of some semilinear elliptic equations, such…
In this work we consider weakly non-radiative solutions to both linear and non-linear wave equations. We first characterize all weakly non-radiative free waves, without the radial assumption. Then in dimension 3 we show that the initial…
Optimal estimates on asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations \begin{eqnarray*} -\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u+m|u|^{p-2}u=f(u), &…
In this article we study the asymptotic behavior of solutions of some fractional differential equations. We prove convergence to power type functions under some assumptions on the nonlinearities. Our results extend and generalize some…
In this paper, we study the asymptotic behavior as $x_1\to+\infty$ of solutions of semilinear elliptic equations in quarter- or half-spaces, for which the value at $x_1=0$ is given. We prove the uniqueness and characterize the…
We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric.
We study asymptotic behavior of sub-solutions to non-uniformly elliptic equations with nonstandard growth. In particular, Harnack type inequalities are proved. Our approach gives new results for the cases with (p,q) nonlinearity and…
In this paper we study entire radial solutions for the quasilinear $p$-Laplace equation $\Delta_p u + k(x) f(u) = 0$ where $k$ is a radial positive weight and the nonlinearity behaves e.g. as $f(u)=u|u|^{q-2}-u|u|^{Q-2}$ with $q<Q$. In…
Optimal estimates on asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations \begin{eqnarray*} -\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u+m|u|^{p-2}u=f(u), &…
We investigate the structure of branching asymptotics appearing in solutions to elliptic edge problems. The exponents in powers of the half-axis variable, logarithmic terms, and coefficients depend on the variables on the edge and may be…
This paper deals with the existence of positive radial solutions to the iterative system of nonlinear elliptic equations of the form $$ \begin{aligned} \triangle{\mathtt{u}_{{\dot{\iota}} }}-\frac{(\mathtt{N}-2)^2r_0^{2\mathtt{N}-2}}{\vert…
The present work has two objectives. First, we prove that a weight\-ed superlinear elliptic problem has infinitely many nonradial solutions in the unit ball. Second, we obtain the same conclusion in annuli for a more general nonlinearity…
We consider a nonlinear parabolic equation with an exponential nonlinearity which is critical with respect to the growth of the nonlinearity and the regularity of the initial data. After showing the equivalence of the notions of weak and…
Asymptotics of solutions to Schroedinger equations with singular dipole-type potentials is investigated. We evaluate the exact behavior near the singularity of solutions to elliptic equations with potentials which are purely angular…
In this article we study the asymptotic behavior, of the solution of a nonlinear elliptic, anisotropic singular perturbations problem in cylindrical domain, the limit problem is given and strong convergences are proved, we also give an…
We investigate asymptotic behavior of solutions for nonlocal elliptic boundary value problems in plane angles and in ${\mathbb R}^2\backslash\{0\}$. Such problems arise as model ones when studying asymptotics of solutions for nonlocal…
We use a method, inspired by Pohozeav's work, to study asymptotic behaviors of non-variational elliptic systems in dimension n greater than two. The results apply to changing sign solutions.