Results 71 to 80 of about 4,702,923 (209)
Multiple solutions for weighted Kirchhoff equations involving critical Hardy-Sobolev exponent
, 2020 In this article, we consider a class of Kirchhoff equations with critical Hardy-Sobolev exponent and indefinite nonlinearity, which has not been studied in the literature. We prove very nicely that this equation has at least two solutions in ℝ3. And some
Shen Zupei +3 more
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Well‐posedness of heat equations with nonlinearities of arbitrarily rapid growth
Proceedings of the London Mathematical Society, Volume 133, Issue 3, September 2026.Abstract We address local‐ and global‐in‐time well‐posedness of the Cauchy problem for nonlinear heat equations without imposing growth rate restrictions on the nonlinearity a priori. Our results constitute a nontrivial expansion of the classical Lq$L^q$‐theory for nonlinearities dominated by polynomial growth and the exponential‐Orlicz space theory ...
Yohei Fujishima +2 more
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A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces. [PDF]
, 2004 We study the Poincaré inequality in Sobolev spaces with variable exponent. Under a rather mild and sharp condition on the exponent p we show that the inequality holds. This condition is satisfied e. g.
Hästö, Peter, Harjulehto, Petteri
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Mathematical Methods in the Applied Sciences, Volume 49, Issue 12, Page 13324-13360, August 2026.ABSTRACT This paper proves the existence of nontrivial solution for two classes of quasilinear systems of the type −ΔΦ1u=Fu(x,u,v)+λRu(x,u,v)inΩ−ΔΦ2v=−Fv(x,u,v)−λRv(x,u,v)inΩu=v=0on∂Ω$$ \left\{\begin{array}{l}\hfill -{\Delta}_{\Phi_1}u={F}_u\left(x,u,v\right)+\lambda {R}_u\left(x,u,v\right)\kern0.1832424242424242em \mathrm{in}\kern0.3em \Omega ...
Lucas da Silva, Marco Souto
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On elliptic systems with Sobolev critical exponent
Discrete and Continuous Dynamical Systems, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Unified Framework From Boltzmann Transport to Proton Treatment Planning
Studies in Applied Mathematics, Volume 157, Issue 2, August 2026.ABSTRACT We develop a unified stochastic–deterministic framework for proton transport in radiotherapy. The deterministic formulation is based on a Boltzmann–Fokker–Planck (BFP) equation with continuous slowing‐down, angular diffusion, and scattering terms, posed in a kinetic variational setting.
Andreas E. Kyprianou +2 more
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Critical Sobolev exponent problem in Rn(n≥4) with Neumann boundary condition
, 1990 In this paper we study the existence and non existence of positive solution for the critical Sobolev exponent problem - Δu = u(n+2)/(n-2) + λα(x)u) in Ω ∂u/∂c = 0 on ∂B, where Ω is a bounded domain in Rn(n≥
Yadava, S. L., Adimurthi
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Mizohata–Takeuchi inequalities for orthonormal systems
Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.Abstract We establish some weighted L2$L^2$ inequalities for Fourier extension operators in the setting of orthonormal systems. In the process, we develop a direct approach to such inequalities based on generalized Wigner distributions, complementing the Schatten space approach that is prevalent in the wider context of estimates for such orthonormal ...
Jonathan Bennett +4 more
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A note on problems involving critical Sobolev exponents
Differential and Integral Equations, 1995 Existence of a nontrivial solution of the semilinear elliptic equation \(- \Delta u= | u|^{p-2} u+ f(x,u)\) in \(G\), \(u=0\) on \(\partial G\) is shown in this paper. Here \(G\) denotes a smooth bounded domain in \(\mathbb{R}^ N\) \((N\geq 4)\), \(p-1= (N+2)/ (N-2)\) (the so-called critical Sobolev exponent) and \(f(x,u)= \lambda u+ g(x,u)\) is ...
Costa, D. G., Silva, E. A.
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Low eigenvalues of the p$p$–Laplacian in general open sets
Journal of the London Mathematical Society, Volume 114, Issue 2, August 2026.Abstract We consider the minmax Ljusternik–Schnirelmann levels of the constrained p$p$–Dirichlet integral on a general open set of the Euclidean space. We show that, whenever one of these levels lies below the threshold given by the Lp$L^p$ Poincaré constant “at infinity,” it actually defines an eigenvalue of the Dirichlet p$p$–Laplacian. We also prove
Lorenzo Brasco +2 more
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