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In this paper, we prove the existence of infinitely many solutions for a class of quasilinear elliptic $m(x)$-polyharmonic Kirchhoff equations where the nonlinear function has a quasicritical growth at infinity and without assuming the Ambrosetti and
Externí odkaz:
http://arxiv.org/abs/2106.07705
Existence and nonexistence results of polyharmonic boundary value problems with supercritical growth
We establish some existence results of polyharmonic boundary value problems with supercritical growth. Our approach is based on truncation argument as well as $L^{\infty}$-bounds. Also, by virtue of Pucci-serrin's variational identity \cite{PS}, we p
Externí odkaz:
http://arxiv.org/abs/2106.03920
Autor:
Harrabi, Abdellaziz
We investigate {\bf explicit} universal estimate of finite Morse index solutions to polyharmonic equations. \,Differently to previous works \cite{BL2, DDF, fa, H1}, propose here a direct proof using a new interpolation inequality and a delicate boot-
Externí odkaz:
http://arxiv.org/abs/2105.04058
Consider the following $m-$polyharmonic Kirchhoff problem: \begin{eqnarray} \label{ea} \begin{cases} M\left(\int_{\O}|D_r u|^{m} +a|u|^m\right)[\Delta^r_m u +a|u|^{m-2}u]= K(x)f(u) &\mbox{in}\quad \Omega, \\ u=\left(\frac{\partial}{\partial \nu}\righ
Externí odkaz:
http://arxiv.org/abs/1807.11040
Akademický článek
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We examine the general weighted Lane-Emden system \begin{align*} -\Delta u = \rho(x)v^p,\quad -\Delta v= \rho(x)u^\theta, \quad u,v>0\quad \mbox{in }\;\mathbb{R}^N \end{align*} where $1
Externí odkaz:
http://arxiv.org/abs/1511.06736
In this paper, we establish $L^{\infty}$ and $L^{p}$ estimates for solutions of some polyharmonic elliptic equations via the Morse index. As far as we know, it seems to be the first time that such explicit estimates are obtained for polyharmonic prob
Externí odkaz:
http://arxiv.org/abs/1511.04907
Publikováno v:
Mathematical Methods in the Applied Sciences; 7/30/2024, Vol. 47 Issue 11, p8490-8499, 10p
Autor:
Harrabi, Abdellaziz
We introduce tow assumptions weaker than the classical Ambrosetti-Rabinowitz and the subcritical polynomial growth conditions to obtain the Palais-Smale Condition. Therefore, we improve the Ambrosetti- Rabinowitz existence theorems. Also, we prove so
Externí odkaz:
http://arxiv.org/abs/1310.7743
Akademický článek
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