Related papers: Critical exponent and sharp lifespan estimates for…
In this paper, we establish temporal decay for a weak solution $u(x,t)$ (with initial data $u_0$) of the Navier-Stokes equations with supercritical fractional dissipation $\alpha \in (0,\frac{5}{4})$ in $L^2(\mathbb{R}^3)$ and…
Pseudo-$\epsilon$ expansions ($\tau$-series) for critical exponents of 3D XY model describing $\lambda$-transition in liquid helium are derived up to $\tau^6$ terms. Numerical estimates extracted from the $\tau$-series obtained using…
This paper is devoted to studying the following two initial-boundary value problems for semilinear wave equations with variable coefficients on exterior domain with subcritical exponent in $n$ space dimensions:…
In this paper we consider the following class of fractional Kirchhoff equations with critical growth: \begin{equation*} \left\{ \begin{array}{ll}…
We consider the natural time-dependent fractional $p$-Laplacian equation posed in the whole Euclidean space, with parameter $1<p<2$ and fractional exponent $s\in (0,1)$. Rather standard theory shows that the Cauchy Problem for data in the…
In this paper, by an approximating argument, we obtain infinitely many solutions for the following Hardy-Sobolev fractional equation with critical growth \begin{equation*}\label{0.1} \left\{% \begin{array}{ll} (-\Delta)^{s} u-\ds\frac{\mu…
This article deals with the problems of local and global solvability for a semilinear heat equation on the Heisenberg group involving a mixed local and nonlocal nonlinearity. The characteristic features of such equations, arising from the…
We discuss recent advances in the theory of quasilinear equations of the type $ -\Delta_{p} u = \sigma u^{q} \; \; \text{in} \;\; \mathbb{R}^n, $ in the case $0<q< p-1$, where $\sigma$ is a nonnegative measurable function, or measure, for…
In this paper, we are interested in studying the multiplicity, uniqueness, and nonexistence of solutions for a class of singular elliptic eigenvalue problem for the Dirichlet fractional $(p,q)$-Laplacian. The nonlinearity considered…
In this paper we consider semilinear equations $-\Delta u=f(u)$ with Dirichlet boundary conditions on certain convex domains of the two dimensional model spaces of constant curvature. We prove that a positive, semi-stable solution $u$ has…
In this paper we study the problem of bifurcation from the origin of solutions of elliptic Dirichlet problems involving critical Sobolev exponent, defined on a bounded domain $\Omega$ in $\mathbb{R} ^N$: we prove that the first critical…
In this paper, we study the Cauchy problems for weakly coupled systems of semi-linear structurally damped $\sigma$-evolution models with different power nonlinearities. By assuming additional $L^m$ regularity on the initial data, with $m…
We consider the semilinear elliptic boundary value problem \[ -\Delta u=\left\vert u\right\vert ^{p-2}u\text{ in }\Omega,\text{\quad }u=0\text{ on }\partial\Omega, \] in a bounded smooth domain $\Omega$ of $\mathbb{R}^{N}$ for supercritical…
This note establishes sharp time-asymptotic algebraic rate bounds for the classical evolution problem of Fujita, but with sublinear rather than superlinear exponent. A transitional stability exponent is identified, which has a simple…
We prove the existence of solution for a class of $p(x)$-Laplacian equations where the nonlinearity has a critical growth. Here, we consider two cases: the first case involves the situation where the variable exponents are periodic…
In the present paper, we study small data blow-up of the semi-linear wave equation with a scattering dissipation term and a time-dependent mass term from the aspect of wave-like behavior. The Strauss type critical exponent is determined and…
By using the Strichartz esitmate and Picard iteration, we prove the subcritical(critical in some cases) global solution in $C_t H_x^s\cap C_t^1 H^{s-1}_x$ with small data for semilinear wave equation with nonlinearity of type $(\partial…
We consider semilinear evolution equations of the form $a(t)\partial_{tt}u + b(t) \partial_t u + Lu = f(x,u)$ and $b(t) \partial_t u + Lu = f(x,u),$ with possibly unbounded $a(t)$ and possibly sign-changing damping coefficient $b(t)$, and…
In this paper we prove the existence of at least one positive solution for the nonlocal semipositone problem \[ \displaystyle \left\{\begin{array}{rcll} (-\Delta)_p^s(u) &=& \lambda f(u) \qquad & \text{in} \ \ \Omega \\u &=& 0 & \text{in} \…
We obtain new estimates for the existence time of the maximal solutions to the nonlinear heat equation $\partial_tu-\Delta u=|u|^\alpha u,\;\alpha>0$ with initial values in Lebesgue, weighted Lebesgue spaces or measures. Non-regular,…