Results 31 to 40 of about 4,486,095 (208)
The concentration-compactness principles for Ws,p(·,·)(ℝN) and application
Advances in Nonlinear Analysis, 2020 We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems ...
Ho Ky, Kim Yun-Ho
doaj +1 more source
A Test Function Method for Weakly Coupled Systems With Derivative‐Type Nonlinearity
Mathematische Nachrichten, EarlyView.ABSTRACT We consider a two by two system of inequalities which include fractional powers of the Laplace operator, coupled through a semilinear term of derivative type. We prove the nonexistence of global‐in‐time weak solutions for powers below the critical curve and possibly on the critical curve.
Marcello D'Abbicco, Antonio Lagioia
wiley +1 more source
Resultados de existência para equações elípticas com termos singulares [PDF]
, 2013 Doutoramento em Matemática e AplicaçõesEsta dissertação estuda em detalhe três problemas elípticos: (I) uma classe de equações que envolve o operador Laplaciano, um termo singular e nãolinearidade com o exponente crítico de Sobolev, (II) uma classe de ...
Murillo, Kelly Patricia
core
A singular perturbed problem with critical Sobolev exponent
Topological Methods in Nonlinear Analysis, 2021 This paper deals with the following nonlinear elliptic problem \begin{equation}\label{eq0.1} -\varepsilon^2\Delta u+\omega V(x)u=u^{p}+u^{2^{*}-1},\quad u> 0\quad\text{in}\ \R^N, \end{equation} where $\omega\in\R^{+}$, $N\geq 3$, $p\in (1,2^{*}-1)$ with $2^{*}={2N}/({N-2})$, $\varepsilon> 0$ is a small parameter and $V(x)$ is a given function ...
Mengyao Chen, Qi Li
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Performance of a Mixed Least‐Squares Finite Element Formulation With Application in Poroelasticity
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.ABSTRACT A mixed least‐squares finite element method (LSFEM), previously proposed for the theory of porous media (TPM), is further investigated in this work. Finite deformation of a fully saturated, incompressible solid–fluid binary system is studied using the LSFEM.
Manu Hegde +3 more
wiley +1 more source
A weighted Hardy-Sobolev-Maz’ya inequality [PDF]
, 2014 We provide a weighted extension of a Hardy-Sobolev-Maz’ya inequality that is due to Filippas, Maz’ya and ...
Sourdis, Christos
core
Strongly indefinite systems with critical Sobolev exponents [PDF]
Transactions of the American Mathematical Society, 1998 We consider an elliptic system of Hamiltonian type on a bounded domain. In the superlinear case with critical growth rates we obtain existence and positivity results for solutions under suitable conditions on the linear terms. Our proof is based on an adaptation of the dual variational method as applied before to the scalar case.
MITIDIERI, ENZO +2 more
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Solvability and Boundedness in Chemotaxis‐Consumption Models With Oppositely Acting Nonlocal Sources
Mathematical Methods in the Applied Sciences, Volume 49, Issue 14, Page 16146-16162, 30 September 2026.ABSTRACT In this paper, we investigate a chemotaxis system featuring a class of external source terms that incorporate both local and nonlocal growth as well as dampening effects. The model describes the evolution of a cell density u$$ u $$, which migrates in response to a chemical signal v$$ v $$, within an impermeable habitat.
Rafael Díaz Fuentes +3 more
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Fourth order Hardy-Sobolev equations: Singularity and doubly critical exponent [PDF]
, 2023 In dimension $N\geq 5$, and for ...
Ali, Hussein Cheikh
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Advanced Materials, Volume 38, Issue 51, 11 September 2026.Residual magnetization induces pronounced mechanical anisotropy in ultra‐soft magnetorheological elastomers, shaping deformation and actuation even without external magnetic fields. This study introduces a computational‐experimental framework integrating magneto‐mechanical coupling into topology optimization for designing soft magnetic actuators with ...
Carlos Perez‐Garcia +3 more
wiley +1 more source