Results 31 to 40 of about 95 (88)
Mathematics, 2019 We study the following quasilinear Schrödinger equation involving critical exponent − Δ u + V ( x ) u − Δ ( u 2 ) u = A ( x ) | u | p − 1 u + λ B ( x ) u 3 N + 2 N − 2 , u ( x
Jianqing Chen, Qian Zhang
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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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Domain geometry and the Pohozaev identity
Electronic Journal of Differential Equations, 2005 In this paper, we investigate the boundary between existence and nonexistence for positive solutions of Dirichlet problem $Delta u + f(u) = 0$, where $f$ has supercritical growth.
Gregg Stubbendieck +3 more
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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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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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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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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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Existence of Normalized Solutions of a Hartree–Fock System With Mass Subcritical Growth
Mathematical Methods in the Applied Sciences, Volume 48, Issue 12, Page 12309-12319, August 2025.ABSTRACT In this paper, we are concerned with normalized solutions of a class of Hartree‐Fock type systems. By seeking the constrained global minimizers of the corresponding functional, we prove that the existence and nonexistence of normalized solutions.
Hua Jin +3 more
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Ground states of a non‐local variational problem and Thomas–Fermi limit for the Choquard equation
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract We study non‐negative optimisers of a Gagliardo–Nirenberg‐type inequality ∫∫RN×RN|u(x)|p|u(y)|p|x−y|N−αdxdy⩽C∫RN|u|2dxpθ∫RN|u|qdx2p(1−θ)/q,$$\begin{align*} & \iint\nolimits _{\mathbb {R}^N \times \mathbb {R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-\alpha }} dx\, dy\\ &\quad \leqslant C{\left(\int _{{\mathbb {R}}^N}|u|^2 dx\right)}^{p\theta } {\
Damiano Greco +3 more
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