Results 31 to 40 of about 160 (129)
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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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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(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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Numerical Study of a Nonlocal Nonlinear Schrödinger Equation (MMT Model)
Studies in Applied Mathematics, Volume 156, Issue 3, March 2026.ABSTRACT In this paper, we study a nonlocal nonlinear Schrödinger equation (MMT model). We investigate the effect of the nonlocal operator appearing in the nonlinearity on the long‐term behavior of solutions, and we identify the conditions under which the solutions of the Cauchy problem associated with this equation are bounded globally in time in the ...
Amin Esfahani, Gulcin M. Muslu
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Cazenave‐Dickstein‐Weissler‐Type Extension of Fujita'S Problem on Heisenberg Groups
Mathematical Methods in the Applied Sciences, Volume 49, Issue 2, Page 499-511, 30 January 2026.ABSTRACT This paper investigates the Fujita critical exponent for a heat equation with nonlinear memory posed on the Heisenberg groups. A sharp threshold is identified such that, for exponent values less than or equal to this critical value, no global solution exists, regardless of the choice of nonnegative initial data. Conversely, for exponent values
Mokhtar Kirane +3 more
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Non-existence of positive radial solution for semipositone weighted p-Laplacian problems
Electronic Journal of Differential Equations, 2015 We prove the non-existence of positive radial solution to a semipositone weighted $p$-Laplacian problem whenever the weight is sufficiently large. Our main tools are a Pohozaev type identity and a comparison principle.
Sigifredo Herron, Emer Lopera
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Normalized solutions of the critical Schrödinger–Bopp–Podolsky system with logarithmic nonlinearity
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract In this paper, we study the following critical Schrödinger–Bopp–Podolsky system driven by the p$p$‐Laplace operator and a logarithmic nonlinearity: −Δpu+V(εx)|u|p−2u+κϕu=λ|u|p−2u+ϑ|u|p−2ulog|u|p+|u|p*−2uinR3,−Δϕ+a2Δ2ϕ=4π2u2inR3.$$\begin{equation*} {\begin{cases} -\Delta _p u+\mathcal {V}(\varepsilon x)|u|^{p-2}u+\kappa \phi u=\lambda |u|^{p-2 ...
Sihua Liang +3 more
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Some constancy results for harmonic maps from non-contractable domains into spheres
Electronic Journal of Differential Equations, 2000 We use the Pohozaev identity on sub-domains of a Euclidean $r$-neighbourhood for a closed or broken curve to show that harmonic maps from such domains into spheres with constant boundary value remain constant.
Kewei Zhang
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Brezis–Nirenberg type results for the anisotropic p$p$‐Laplacian
Journal of the London Mathematical Society, Volume 112, Issue 4, October 2025.Abstract In this paper, we consider a quasilinear elliptic and critical problem with Dirichlet boundary conditions in presence of the anisotropic p$p$‐Laplacian. The critical exponent is the usual p★$p^{\star }$ such that the embedding W01,p(Ω)⊂Lp★(Ω)$W^{1,p}_{0}(\Omega) \subset L^{p^{\star }}(\Omega)$ is not compact.
Stefano Biagi +3 more
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