ترغب بنشر مسار تعليمي؟ اضغط هنا

Variational approach to the existence of solutions for non-instantaneous impulsive differential equations with perturbation

57   0   0.0 ( 0 )
 نشر من قبل Jing Zeng
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper, we study the existence of solutions for second-order non-instantaneous impulsive differential equations with a perturbation term. By variational approach, we obtain the problem has at least one solution under assumptions that the nonlinearities are super-quadratic at infinity, and sub-quadratic at the origin.



قيم البحث

اقرأ أيضاً

We consider a nonlinear Dirichlet problem driven by the $(p,q)$-Laplacian and with a reaction which is parametric and exhibits the combined effects of a singular term and of a superdiffusive one. We prove an existence and nonexistence result for posi tive solutions depending on the value of the parameter $lambda in overset{circ}{mathbb{R}}_+=(0,+infty)$.
By employing a novel perturbation approach and the method of invariant sets of descending flow, this manuscript investigates the existence and multiplicity of sign-changing solutions to a class of semilinear Kirchhoff equations in the following form $$ -left(a+ bint_{R^3}| abla u|^2right)triangle {u}+V(x)u=f(u),,,xinR^3, $$ where $a,b>0$ are constants, $Vin C(R^3,R)$, $fin C(R,R)$. The methodology proposed in the current paper is robust, in the sense that, the monotonicity condition for the nonlinearity $f$ and the coercivity condition of $V$ are not required. Our result improves the study made by Y. Deng, S. Peng and W. Shuai ({it J. Functional Analysis}, 3500-3527(2015)), in the sense that, in the present paper, the nonlinearities include the power-type case $f(u)=|u|^{p-2}u$ for $pin(2,4)$, in which case, it remains open in the existing literature that whether there exist infinitely many sign-changing solutions to the problem above without the coercivity condition of $V$. Moreover, {it energy doubling} is established, i.e., the energy of sign-changing solutions is strictly large than two times that of the ground state solutions for small $b>0$.
259 - Loic Le Treust 2012
We prove, by a shooting method, the existence of infinitely many solutions of the form $psi(x^0,x) = e^{-iOmega x^0}chi(x)$ of the nonlinear Dirac equation {equation*} iunderset{mu=0}{overset{3}{sum}} gamma^mu partial_mu psi- mpsi - F(bar{psi}psi)psi = 0 {equation*} where $Omega>m>0,$ $chi$ is compactly supported and [F(x) = {{array}{ll} p|x|^{p-1} & text{if} |x|>0 0 & text{if} x=0 {array}.] with $pin(0,1),$ under some restrictions on the parameters $p$ and $Omega.$ We study also the behavior of the solutions as $p$ tends to zero to establish the link between these equations and the M.I.T. bag model ones.
We classify positive solutions to a class of quasilinear equations with Neumann or Robin boundary conditions in convex domains. Our main tool is an integral formula involving the trace of some relevant quantities for the problem. Under a suitable con dition on the nonlinearity, a relevant consequence of our results is that we can extend to weak solutions a celebrated result obtained for stable solutions by Casten and Holland and by Matano.
212 - Guo-cheng Wu 2010
Fractional variational approach has gained much attention in recent years. There are famous fractional derivatives such as Caputo derivative, Riesz derivative and Riemann-Liouville derivative. Sever
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا