Results 31 to 40 of about 159 (128)
Finite Morse index solutions of the Hénon Lane–Emden equation
Journal of Inequalities and Applications, 2019 In this paper, we are concerned with Liouville-type theorems of the Hénon Lane–Emden triharmonic equations in whole space. We prove Liouville-type theorems for solutions belonging to one of the following classes: stable solutions and finite Morse index ...
Abdellaziz Harrabi, Cherif Zaidi
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On the Pohozaev identity for quasilinear Finsler anisotropic equations
, 2022 In this paper we derive the Pohozaev identity for quasilinear equations \begin{equation}\tag{$E$}\label{eq:p} -\operatorname{div}(B'(H(\nabla u))\nabla H(\nabla u))=g(x, u) \quad \text {in}\,\, Ω, \end{equation} involving the anisotropic Finsler operator $-\operatorname{div}(B'(H(\nabla u))\nabla H(\nabla u))$.
Montoro, Luigi, Sciunzi, Berardino
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Electronic Journal of Qualitative Theory of Differential EquationsIn this paper, we consider the existence and nonexistence of solutions for a class of modified Schrödinger–Poisson system with Kirchhoff-type perturbation by use of variational methods.
Yaru Wang, Jing Zhang
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UNIVERSAL PRINCIPLES FOR KAZDAN–WARNER AND POHOZAEV–SCHOEN TYPE IDENTITIES [PDF]
Communications in Contemporary Mathematics, 2013 The classical Pohozaev identity constrains potential solutions of certain semilinear PDE boundary value problems. The Kazdan–Warner identity is a similar necessary condition important for the Nirenberg problem of conformally prescribing scalar curvature on the sphere. For dimensions n ≥ 3 both identities are captured and extended by a single identity,
Gover, Rod, Orsted, Bent
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Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2021 The aim of this paper is to present a version of the generalized Pohozaev-Schoen identity in the context of asymptotically Euclidean manifolds. Since these kind of geometric identities have proven to be a very powerful tool when analysing different geometric problems for compact manifolds, we will present a variety of applications within this new ...
R. Avalos, A. Freitas
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Mathematische Nachrichten, Volume 299, Issue 5, Page 1004-1027, May 2026.ABSTRACT This paper investigates the existence and non‐existence and uniqueness of global solutions for certain parameter values c$c$ in a new class of generalized fractional p$p$‐Kirchhoff equations in the whole space. Using the Pohozaev and Nehari identities for an auxiliary problem, together with the fractional Gagliardo–Nirenberg inequality and the
J. Vanterler da C. Sousa +2 more
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Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.ABSTRACT We study the nonlinear Schrödinger equation with a competing cubic–quintic power‐law nonlinearity on the waveguide domain Rx×TLy$\mathbb {R}_x \times \mathbb {T}_{L_y}$. This model is globally well‐posed and admits line solitary wave solutions, whose transverse (in‐)stability is numerically investigated.
Christian Klein, Christof Sparber
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Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract In this paper, we investigate the following D1,p$D^{1,p}$‐critical quasi‐linear Hénon equation involving p$p$‐Laplacian −Δpu=|x|αupα∗−1,x∈RN,$$\begin{equation*} -\Delta _p u=|x|^{\alpha }u^{p_\alpha ^*-1}, \qquad x\in \mathbb {R}^N, \end{equation*}$$where N⩾2$N\geqslant 2$, 1
Wei Dai +3 more
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(N,q)$(N,q)$‐Laplacian equations with one‐sided critical exponential growth
Mathematische Nachrichten, Volume 299, Issue 3, Page 675-698, March 2026.Abstract We prove the existence of two non‐trivial weak solutions for a class of quasilinear, non‐homogeneous elliptic problems driven by the (N,q)$(N,q)$‐Laplacian with one‐sided critical exponential growth in a bounded domain Ω⊂RN$\Omega \subset \mathbb {R}^{N}$. The first solution is obtained as a local minimizer of the associated energy functional;
Elisandra Gloss +2 more
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Abstract and Applied Analysis, 2014 We consider system of integral equations related to the weighted Hardy-Littlewood-Sobolev (HLS) inequality in a half space. By the Pohozaev type identity in integral form, we present a Liouville type theorem when the system is in both supercritical and ...
Linfen Cao, Zhaohui Dai
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