Results 81 to 90 of about 12,172 (236)

Existence and multiplicity of solutions for divergence type elliptic equations

Electronic Journal of Differential Equations, 2011
We establish the existence and multiplicity of weak solutions of a problem involving a uniformly convex elliptic operator in divergence form. We find one nontrivial solution by the mountain pass lemma, when the nonlinearity has a $(p-1)$-superlinear ...
Lin Zhao, Peihao Zhao, Xiaoxia Xie
doaj  

Positive solutions of a derivative dependent second-order problem subject to Stieltjes integral boundary conditions

Electronic Journal of Qualitative Theory of Differential Equations, 2019
In this paper, we investigate the derivative dependent second-order problem subject to Stieltjes integral boundary conditions \begin{equation*} \begin{cases}-u''(t)=f(t,u(t),u'(t)),\quad t\in[0,1],\\ au(0)-bu'(0)=\alpha[u],\ cu(1)+du'(1)=\beta[u],\end ...
Zhongyang Ming, Guowei Zhang, Hongyu Li
doaj   +1 more source

Duality and calculi without exceptions for convex objects [PDF]

The aim of this paper is to make a contribution to theinvestigation of the roots and essence of convex analysis, and tothe development of the duality formulas of convex calculus.
Brinkhuis, J.
core   +1 more source

Weighted anisotropic product Hardy spaces and boundedness of sublinear operators

Mathematische Nachrichten, 2010
AbstractLet A1 and A2 be expansive dilations, respectively, on ℝn and ℝm. Let A ≡ (A1, A2) and 𝒜p(A) be the class of product Muckenhoupt weights on ℝn × ℝm for p ∈ (1, ∞]. When p ∈ (1, ∞) and w ∈ 𝒜p(A), the authors characterize the weighted Lebesgue space Lp w(ℝn × ℝm) via the anisotropic Lusin‐area function associated with A. When p ∈ (0, 1], w ∈ 𝒜∞(A)
Bownik, Marcin, Li, Baode, Yang, Dachun, Zhou, Yuan   +3 more
openaire   +2 more sources

Minimal Lp-solutions to singular sublinear elliptic problems

Results in Applied Mathematics
We solve the existence problem for the minimal positive solutions u∈Lp(Ω,dx) to the Dirichlet problems for sublinear elliptic equations of the form Lu=σuq+μinΩ,lim infx→yu(x)=0y∈∂∞Ω,where ...
Aye Chan May, Adisak Seesanea
doaj   +1 more source

Lepskii Principle in Supervised Learning

, 2019
In the setting of supervised learning using reproducing kernel methods, we propose a data-dependent regularization parameter selection rule that is adaptive to the unknown regularity of the target function and is optimal both for the least-square ...
Blanchard, Gilles, Mathé, Peter, Mücke, Nicole   +2 more
core  

BOUNDEDNESS CRITERION FOR SUBLINEAR OPERATORS AND COMMUTATORS ON GENERALIZED MIXED MORREY SPACES

, 2022
Mingquan Wei
openalex   +1 more source

Nonhomogeneous quasilinear elliptic systems with small perturbations and lack of compactness

Bulletin of Mathematical Sciences
We investigate a class of quasilinear elliptic system involving a nonhomogeneous differential operator which is introduced by Stuart [Milan J. Math. 79 (2011) 327–341] and depends not only on [Formula: see text] but also on u.
Xingyong Zhang, Wanting Qi
doaj   +1 more source

An existence results of a product type fractional functional integral equations using Petryshyn's fixed point theorem

Journal of Taibah University for Science
In this paper, we investigate the existence of solutions for a new class of nonlinear product-type fractional functional integral equations (FFIEs) involving the Riemann–Liouville fractional integral operator.
Sukanta Halder, Deepmala, Cemil Tunç
doaj   +1 more source

On a conic approach to convex analysis. [PDF]

. The aim of this paper is to make an attempt to justify the main results from Convex Analysis by one elegant tool, the conification method, which consists of three steps: conify, work with convex cones, deconify.
Brinkhuis, J.
core   +1 more source