DAMMAK, M., EL Ghord, M. (2016). Bifurcation problem for biharmonic asymptotically linear elliptic equation. Theory of Approximation and Applications, (), -.

Makkia DAMMAK; Majdi EL Ghord. "Bifurcation problem for biharmonic asymptotically linear elliptic equation". Theory of Approximation and Applications, , , 2016, -.

DAMMAK, M., EL Ghord, M. (2016). 'Bifurcation problem for biharmonic asymptotically linear elliptic equation', Theory of Approximation and Applications, (), pp. -.

DAMMAK, M., EL Ghord, M. Bifurcation problem for biharmonic asymptotically linear elliptic equation. Theory of Approximation and Applications, 2016; (): -.

Bifurcation problem for biharmonic asymptotically linear elliptic equation

Articles in Press, Accepted Manuscript , Available Online from 12 July 2016

In this paper, we investigate the existence of positive solutions for the elliptic equation $Delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $Omega$ of $R^{n}$, $ngeq2$, with Navier boundary conditions. Here $lambda>0$ is a parameter, $c(x)$ is positive continuous function defined on $Omega$ and $f$ is a $C^{1}$ function, defined on $[0,+infty)$, positive, nondecreasing, convex and asymptotically linear that is ${lim_{t rightarrow infty}}frac{f(t)}{t}=a0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution but for $lambda> lambda^{ast}$, the problem has no solution even in the week sense. For $lambda = lambda^{ast}$, the problem has a solution said extremal provided that $ lim_{trightarrowinfty}f(t)-at=l

Bifurcation problem for biharmonic asymptotically linear elliptic equations

Authors [Persian]

Makkia Dammak^{1}; Majid EL Ghord^{2}

^{}

^{2}Universty of Tunis El Manar

Abstract [Persian]

In this paper, we investigate the existence of positive solutions for the elliptic equation $Delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $Omega$ of $R^{n}$, $ngeq2$, with Navier boundary conditions. Here $lambda>0$ is a parameter, $c(x)$ is positive continuous function defined on $Omega$ and $f$ is a $C^{1}$ function, defined on $[0,+infty)$, positive, nondecreasing, convex and asymptotically linear that is ${lim_{t rightarrow infty}}frac{f(t)}{t}=a0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution but for $lambda> lambda^{ast}$, the problem has no solution even in the week sense. For $lambda = lambda^{ast}$, the problem has a solution said extremal provided that $ lim_{trightarrowinfty}f(t)-at=l