A non-local non-autonomous diffusion problem: linear and sublinear cases

In this paper we study a stationary problem arising from population dynamics with a local and nonlocal variable diffusion coefficient. We show the existence of an unbounded continuum of positive solutions that bifurcates from the trivial solution. The global structure of this continuum depends on the value of the nonlocal diffusion at infinity and the relative position of the refuge of the species and of the sets where it diffuses locally and not locally, respectively.

show abstract

“…The first case (D 2 = ∅) is the classical eigenvalue problem, and hence the result is well-known. The second one follows by [9].…”

Section: Figueiredo Figueiredo-sousa Morales-rodrigo and Suárezmentioning

confidence: 90%

“…Then, we can take K large enough verifying (9) and (10). Moreover, we can choose small and K large so that u ≤ u in Ω, and we obtain the existence of positive solution of (7).…”

mentioning

confidence: 99%

Existence of positive solutions of an elliptic equation with local and nonlocal variable diffusion coefficient

Figueiredo¹,

Figueiredo-Sousa²,

Suárez³

2019

Discrete &Amp; Continuous Dynamical Systems - B

Self Cite

View full text Add to dashboard Cite

show abstract

“…See, for instance, Chipot-Rodrigues [8]. For papers involving operators as in (GCP ) with p > 1 arbitrary, we refer the reader to Figueiredo-Sousa-Morales-Rodrigo-Suárez [11] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Positive solutions for a class of nonlocal problems with possibly singular nonlinearity

Gasiński¹,

Junior²,

Siciliano³

2020

Preprint

View full text Add to dashboard Cite

We study a class of elliptic problems with homogeneous Dirichlet boundary condition and a nonlinear reaction term f which is nonlocal depending on the L p -norm of the unknown function. The nonlinearity f can make the problem degenerate since it may even have multiple singularities in the nonlocal variable. We use fixed point arguments for an appropriately defined solution map, to produce multiplicity of classical positive solutions with ordered norms.

show abstract

Existence theorems of nontrivial and positive solutions for nonlocal inhomogeneous elliptic problems

Zaouche¹

2021

Ricerche mat

View full text Add to dashboard Cite

A non-local non-autonomous diffusion problem: linear and sublinear cases

Cited by 11 publications

References 19 publications

Existence of positive solutions of an elliptic equation with local and nonlocal variable diffusion coefficient

Existence of positive solutions of an elliptic equation with local and nonlocal variable diffusion coefficient

Positive solutions for a class of nonlocal problems with possibly singular nonlinearity

Existence theorems of nontrivial and positive solutions for nonlocal inhomogeneous elliptic problems

Contact Info

Product

Resources

About