Results 41 to 50 of about 406 (185)

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, HULSHOF J, VAN DER VORST R.   +2 more
openaire   +4 more sources

Existence of Solution for Two Classes of Quasilinear Systems Defined on a Nonreflexive Orlicz–Sobolev Spaces

Mathematical Methods in the Applied Sciences, EarlyView.
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
wiley   +1 more source

Fractional Laplacian equations with critical Sobolev exponent [PDF]

Revista Matemática Complutense, 2015
The paper under review extends in a fractional setting some results concerning the existence of nontrivial solutions for a class of nonlocal elliptic Dirichlet problems involving critical nonlinear terms. The basic analytic tool to establish the existence of a nontrivial solution is the linking method.
Servadei, Raffaella, Valdinoci, Enrico
openaire   +4 more sources

Existence of Solutions of Semilinear Wave Equations With Time‐Dependent Propagation Speed and Time Derivative Nonlinearity

Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 8681-8690, June 2026.
ABSTRACT Consider wave equations with time derivative nonlinearity and time‐dependent propagation speed which are generalized versions of the wave equations in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime, the de Sitter spacetime and the anti‐de Sitter space time.
Kimitoshi Tsutaya, Yuta Wakasugi
wiley   +1 more source

The Choquard Equation with Weighted Terms and Sobolev-Hardy Exponent

Journal of Function Spaces, 2018
We study a nonlinear Choquard equation with weighted terms and critical Sobolev-Hardy exponent. We apply variational methods and Lusternik-Schnirelmann category to prove the multiple positive solutions for this problem.
Yanbin Sang, Xiaorong Luo, Yongqing Wang
doaj   +1 more source

Multiplicity results for biharmonic equations involving multiple Rellich-type potentials and critical exponents

Boundary Value Problems, 2019
In this paper, a biharmonic equation is investigated, which involves multiple Rellich-type potentials and a critical Sobolev exponent. By using variational methods and analytical techniques, the existence and multiplicity of nontrivial solutions to the ...
Jinguo Zhang, Tsing-San Hsu
doaj   +1 more source

Matsumura‐Type Estimates and Global Solutions of a Fractional Wave Equation With Nonlocal Nonlinearity

Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9967-9983, June 2026.
ABSTRACT The main results of this paper are the global existence and long time behavior of solutions of a fractional wave equation with a nonlocal nonlinearity. The techniques in this work rely on norm estimates of the solutions of εutt+ut+(−Δ)βu=0,u(0,x)=φ(x),ut(0,x)=ψ(x),$$ \varepsilon {u}_{tt}+{u}_t+{\left(-\Delta \right)}^{\beta }u=0,\kern1em u ...
Ibrahim Ahmad Suleman, Mokhtar Kirane
wiley   +1 more source

The existence of positive solutions for the Neumann problem of p-Laplacian elliptic systems with Sobolev critical exponent

Boundary Value Problems, 2022
The paper aims to consider a class of p-Laplacian elliptic systems with a double Sobolev critical exponent. We obtain the existence result of the above problem under the Neumann boundary for some suitable range of the parameters in the systems.
Bingyu Kou, Tianqing An
doaj   +1 more source

Building a Digital Twin for Material Testing: Model Reduction and Data Assimilation

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.
ABSTRACT The rapid advancement of industrial technologies, data collection, and handling methods has paved the way for the widespread adoption of digital twins (DTs) in engineering, enabling seamless integration between physical systems and their virtual counterparts.
Rubén Aylwin, Nina Beranek, Gajendra Babu Budihala, Matthias Mettenleiter, Goksu Oruc, Karsten Urban   +5 more
wiley   +1 more source

Normalized solutions for a fractional coupled critical Hartree system

Electronic Journal of Qualitative Theory of Differential Equations
We consider the existence of normalized solutions for a fractional coupled Hartree system, with the upper critical exponent in the sense of the Hardy-Littelwood-Sobolev inequality.
Shengbing Deng, Wenshan Luo
doaj   +1 more source