scholarly journals Trudinger-Moser type inequality and existence of solution for perturbed non-local elliptic operators with exponential nonlinearity

2017 ◽  
Vol 16 (1) ◽  
pp. 243-252 ◽  
Author(s):  
Anouar Bahrouni ◽  
Keyword(s):  
Type Inequality ◽  
Elliptic Operators ◽  
Existence Of Solution ◽  
Exponential Nonlinearity ◽  
Non Local

scholarly journals Pseudo-monotonicity and degenerated or singular elliptic operators

1998 ◽  
Vol 58 (2) ◽  
pp. 213-221 ◽  
Author(s):  
P. Drábek ◽  
A. Kufner ◽  
V. Mustonen
Keyword(s):  
Sobolev Spaces ◽  
Differential Operators ◽  
Weighted Sobolev Spaces ◽  
Type Inequality ◽  
Elliptic Operators ◽  
Hardy Type Inequality ◽  
Hardy Type ◽  
Elliptic Differential Operators

Using the compactness of an imbedding for weighted Sobolev spaces (that is, a Hardy-type inequality), it is shown how the assumption of monotonicity can be weakened still guaranteeing the pseudo-monotonicity of certain nonlinear degenerated or singular elliptic differential operators. The result extends analogous assertions for elliptic operators.

Some remarks on the solvability of non-local elliptic problems with the Hardy potential

2014 ◽  
Vol 16 (04) ◽  
pp. 1350046 ◽  
Author(s):  
B. Barrios ◽  
M. Medina ◽  
I. Peral
Keyword(s):  
Real Number ◽  
Sobolev Inequality ◽  
Positive Real Number ◽  
Fractional Power ◽  
Existence Of Solution ◽  
Sharp Constant ◽  
Hardy Potential ◽  
Positive Real ◽  
Existence And Multiplicity ◽  
Non Local

The aim of this paper is to study the solvability of the following problem, [Formula: see text] where (-Δ)s, with s ∈ (0, 1), is a fractional power of the positive operator -Δ, Ω ⊂ ℝN, N > 2s, is a Lipschitz bounded domain such that 0 ∈ Ω, μ is a positive real number, λ < ΛN,s, the sharp constant of the Hardy–Sobolev inequality, 0 < q < 1 and [Formula: see text], with αλ a parameter depending on λ and satisfying [Formula: see text]. We will discuss the existence and multiplicity of solutions depending on the value of p, proving in particular that p(λ, s) is the threshold for the existence of solution to problem (Pμ).

scholarly journals A Resonance Problem for Non-Local Elliptic Operators

2013 ◽  
Vol 32 (4) ◽  
pp. 411-431 ◽  
Author(s):  
Alessio Fiscella ◽  
Raffaella Servadei ◽  
Enrico Valdinoci
Keyword(s):  
Elliptic Operators ◽  
Resonance Problem ◽  
Non Local

scholarly journals Solvability of BVPs for the Parabolic-Hyperbolic Equation with Non-linear Loaded Term

2021 ◽  
pp. 133-145
Author(s):  
Obidjon Kh. Abdullaev
Keyword(s):  
Hyperbolic Equation ◽  
Existence And Uniqueness ◽  
Type Equation ◽  
Existence Of Solution ◽  
Hyperbolic Type ◽  
Uniqueness Of Solution ◽  
Method Of Integral Equations ◽  
Non Local ◽  
Integral Energy ◽  
Loaded Term

This work is devoted to prove the existence and uniqueness of solution of BVP with non-local assumptions on the boundary and integral gluing conditions for the parabolic-hyperbolic type equation involving Caputo derivatives. Using the method of integral energy, the uniqueness of solution have been proved. Existence of solution was proved by the method of integral equations

Non-local second-order boundary value problems with derivative-dependent nonlinearity

2021 ◽  
Vol 379 (2191) ◽  
pp. 20190383
Author(s):  
J. R. L. Webb
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Term ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
Type Inequality ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Theme Issue ◽  
Non Local

We prove the existence of multiple positive solutions of nonlinear second-order nonlocal boundary value problems with nonlinear term having derivative dependence. We allow the nonlinearity to grow quadratically with respect to derivatives. We obtain a priori bounds for norms of derivatives by using a recently obtained Gronwall-type inequality. Three examples illustrate some of the results. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

scholarly journals Non-local homogenized limits for composite media with highly anisotropic periodic fibres

2006 ◽  
Vol 136 (1) ◽  
pp. 87-114 ◽  
Author(s):  
K. D. Cherednichenko ◽  
V. P. Smyshlyaev ◽  
V. V. Zhikov
Keyword(s):  
Type Inequality ◽  
Double Porosity ◽  
High Contrast ◽  
Composite Media ◽  
Homogenization Problem ◽  
The Matrix ◽  
Non Local ◽  
The Green Function ◽  
Anisotropic Conducting ◽  
Scale Limit

We consider a homogenization problem for highly anisotropic conducting fibres embedded into an isotropic matrix. For a ‘double porosity’-type scaling in the expression of high contrast between the conductivity along the fibres and the conductivities in the transverse directions, we prove the homogenization theorem and derive two-scale homogenized equations using a version of the method of two-scale convergence, supplemented in the case when the spectral parameter λ = 0 by a newly derived variant of high-contrast Poincaré-type inequality. Further elimination of the 'rapid' component from the two-scale limit equations results in a non-local (convolution-type integro-differential) equation for the slowly varying part in the matrix, with the non-local kernel explicitly related to the Green function on the fibre. The regularity of the solution to the non-local homogenized equation is proved.

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