ترغب بنشر مسار تعليمي؟ اضغط هنا

Existence and nonexistence of positive solutions for singular (p,q)-equations with superdiffusive perturbation

121   0   0.0 ( 0 )
 نشر من قبل Patrick Winkert
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

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 positive solutions depending on the value of the parameter $lambda in overset{circ}{mathbb{R}}_+=(0,+infty)$.

قيم البحث

اقرأ أيضاً

In this paper we consider a Dirichlet problem driven by an anisotropic $(p,q)$-differential operator and a parametric reaction having the competing effects of a singular term and of a superlinear perturbation. We prove a bifurcation-type theorem desc ribing the changes in the set of positive solutions as the parameter moves. Moreover, we prove the existence of a minimal positive solution and determine the monotonicity and continuity properties of the minimal solution map.
131 - 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.
This paper deals with existence and regularity of positive solutions of singular elliptic problems on a smooth bounded domain with Dirichlet boundary conditions involving the $Phi$-Laplacian operator. The proof of existence is based on a variant of t he generalized Galerkin method that we developed inspired on ideas by Browder and a comparison principle. By using a kind of Moser iteration scheme we show $L^{infty}(Omega)$-regularity for positive solutions
We study fractional parabolic equations with indefinite nonlinearities $$ frac{partial u} {partial t}(x,t) +(-Delta)^s u(x,t)= x_1 u^p(x, t),,, (x, t) in mathbb{R}^n times mathbb{R}, $$ where $0<s<1$ and $1<p<infty$. We first prove that all positive bounded solutions are monotone increasing along the $x_1$ direction. Based on this we derive a contradiction and hence obtain non-existence of solutions. These monotonicity and nonexistence results are crucial tools in a priori estimates and complete blow-up for fractional parabolic equations in bounded domains. To this end, we introduce several new ideas and developed a systematic approach which may also be applied to investigate qualitative properties of solutions for many other fractional parabolic problems.
This paper deals with the existence of positive solutions for the nonlinear system q(t)phi(p(t)u_{i}(t)))+f^{i}(t,textbf{u})=0,quad 0<t<1,quad i=1,2,...,n. This system often arises in the study of positive radial solutions of nonlinear elliptic syste m. Here $textbf{u}=(u_{1},...,u_{n})$ and $f^{i}, i=1,2,...,n$ are continuous and nonnegative functions, $p(t), q(t)hbox{rm :} [0,1]to (0,oo)$ are continuous functions. Moreover, we characterize the eigenvalue intervals for (q(t)phi(p(t)u_{i}(t)))+lambda h_{i}(t)g^{i} (textbf{u})=0, quad 0<t<1,quad i=1,2,...,n. The proof is based on a well-known fixed point theorem in cones.
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