Multiplicity solutions to non-local problems with general potentials and combined nonlinearities

2021 ◽  
pp. 107583
Author(s):  
Ye Xue
Keyword(s):  
Local Problems ◽  
Non Local

scholarly journals Infinitely many solutions for non-local problems with broken symmetry

2018 ◽  
Vol 7 (3) ◽  
pp. 353-364
Author(s):  
Rossella Bartolo ◽  
Pablo L. De Nápoli ◽  
Addolorata Salvatore
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Problem ◽  
Existence Of Solutions ◽  
Broken Symmetry ◽  
Laplacian Operator ◽  
Infinitely Many Solutions ◽  
Lipschitz Boundary ◽  
Local Problems ◽  
Non Local ◽  
Fractional Laplace Operator

AbstractThe aim of this paper is to investigate the existence of solutions of the non-local elliptic problem\left\{\begin{aligned} &\displaystyle(-\Delta)^{s}u\ =\lvert u\rvert^{p-2}u+h(% x)&&\displaystyle\text{in }\Omega,\\ &\displaystyle{u=0}&&\displaystyle\text{on }\mathbb{R}^{n}\setminus\Omega,\end% {aligned}\right.where {s\in(0,1)}, {n>2s}, Ω is an open bounded domain of {\mathbb{R}^{n}} with Lipschitz boundary {\partial\Omega}, {(-\Delta)^{s}} is the non-local Laplacian operator, {2<p<2_{s}^{\ast}} and {h\in L^{2}(\Omega)}. This problem requires the study of the eigenvalue problem related to the fractional Laplace operator, with or without potential.

scholarly journals The stellar atmosphere physical system II. An operative sequential algorithm to solve the stellar atmosphere problem

2019 ◽  
pp. 1-11
Author(s):  
Lucio Crivellari
Keyword(s):  
Radiative Transfer ◽  
Physical System ◽  
Stellar Atmosphere ◽  
Sequential Algorithm ◽  
Transfer Equations ◽  
Non Linear ◽  
Local Problems ◽  
Equilibrium Constraint ◽  
Non Local ◽  
Radiative Transfer Equations

In this paper, the second and the last of the series, we present a sequential algorithm to solve the stellar atmosphere problem that may serve as a paradigm for the solution of more general non-linear and non-local problems. The Iteration Factors (IF) Method is applied to achieve a solution of the radiative transfer equations, consistent with the radiative equilibrium constraint.

scholarly journals On non-local problems for parabolic equations

1984 ◽  
Vol 93 ◽  
pp. 109-131 ◽  
Author(s):  
J. Chabrowski
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Linear Parabolic Equation ◽  
Local Problem ◽  
Local Problems ◽  
Non Local

The main purposes of this paper are to investigate the existence and the uniqueness of a non-local problem for a linear parabolic equationin a cylinder D = Ω × (0, T].

scholarly journals Some non-local problems with nonlinear diffusion

2011 ◽  
Vol 54 (9-10) ◽  
pp. 2293-2305 ◽  
Author(s):  
Francisco Julio S.A. Corrêa ◽  
Manuel Delgado ◽  
Antonio Suárez
Keyword(s):  
Nonlinear Diffusion ◽  
Local Problems ◽  
Non Local

On the continuity of the solutions of a class of non-local problems for an elliptic equation

1995 ◽  
Vol 186 (2) ◽  
pp. 197-219 ◽  
Author(s):  
A K Gushchin ◽  
V I Mikhailov
Keyword(s):  
Elliptic Equation ◽  
Local Problems ◽  
Non Local

Defect of index in the theory of non-local problems and the $ \eta$-invariant

2004 ◽  
Vol 195 (9) ◽  
pp. 1321-1358 ◽  
Author(s):  
A Yu Savin ◽  
B Yu Sternin
Keyword(s):  
Eta Invariant ◽  
Local Problems ◽  
Non Local

scholarly journals Non-local Problems with Integral Displacement for Highorder Parabolic Equations

2021 ◽  
Vol 36 ◽  
pp. 14-28
Author(s):  
A.I. Kozhanov ◽  
◽  
A.V. Dyuzheva ◽  
◽  
Keyword(s):  
Parabolic Equations ◽  
High Order ◽  
Multidimensional Case ◽  
Integral Conditions ◽  
Spatial Variables ◽  
One Dimensional ◽  
Linear Parabolic Equations ◽  
Local Problems ◽  
Non Local ◽  
The One

The aim of this paper is to study the solvability of solutions of non-local problems with integral conditions in spatial variables for high-order linear parabolic equations in the classes of regular solutions (which have all the squared derivatives generalized by S. L. Sobolev that are included in the corresponding equation) . Previously, similar problems were studied for high-order parabolic equations, either in the one-dimensional case, or when certain conditions of smallness on the coefficients are met equations. In this paper, we present new results on the solvability of non-local problems with integral spatial variables for high-order parabolic equations a) in the multidimensional case with respect to spatial variables; b) in the absence of smallness conditions. The research method is based on the transition from a problem with non-local integral conditions to a problem with classical homogeneous conditions of the first or second kind on the side boundary for a loaded integro-differential equation. At the end of the paper, some generalizations of the obtained results will be described.

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