Another approach to elliptic eigenvalue problems with respect to indefinite weight functions

Heß, Peter; Senn, Stefan

doi:10.1007/bfb0101496

Cited by 8 publications

(8 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the case p = 2, eigenvalue problems of second-order elliptic operator with indefinite weight were studied by many authors. Senn and Hess [10], Hess and Senn [7] studied eigenvalue problems with Neumann boundary conditions. Bandle, Pozio, and Tesei [2] studied the existence and uniqueness of positive solutions to some nonlinear Neumann problems.…”

Section: Introductionmentioning

confidence: 99%

On eigenvalue problems of 𝑝-Laplacian with Neumann boundary conditions

Huang¹

1990

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

On eigenvalue problems of 𝑝-Laplacian with Neumann boundary conditions

Huang¹

1990

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…7). Related results for (non-self-adjoint) elliptic A have been obtained by Hess and Kato in [16] (see also [17] - [19]). [8], [9] - [11], [26] and the vast literature cited in [10].…”

Section: H=-a + Vmentioning

confidence: 54%

On the asymptotic distribution of the eigenvalue branches of the Schrödinger operator HW in a spectral gap of H.

Hempel¹

1989

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

View full text Add to dashboard Cite

“…Furthermore, the following hold for system (22): Proof. In the following, we first prove the theorem assuming that (27) holds.…”

mentioning

confidence: 99%

“…(S1) if one of Cases (A)-(C) holds, then any coexistence steady state of system (22), if it exists, is linearly stable; (22) has no coexistence steady state at all.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Global dynamics of a general Lotka-Volterra competition-diffusion system in heterogeneous environments

Guo¹,

He²,

Ni³

2020

Discrete &Amp; Continuous Dynamical Systems - A

View full text Add to dashboard Cite

Previously in [14], we considered a diffusive logistic equation with two parameters, r(x)-intrinsic growth rate and K(x)-carrying capacity. We investigated and compared two special cases of the way in which r(x) and K(x) are related for both the logistic equations and the corresponding Lotka-Volterra competition-diffusion systems. In this paper, we continue to study the Lotka-Volterra competition-diffusion system with general intrinsic growth rates and carrying capacities for two competing species in heterogeneous environments. We establish the main result that determines the global dynamics of the system under a general criterion. Furthermore, when the ratios of the intrinsic growth rate to the carrying capacity for each species are proportional-such ratios can also be interpreted as the competition coefficients-this criterion reduces to what we obtained in [18]. We also study the detailed dynamics in terms of dispersal rates for such general case. On the other hand, when the two ratios are not proportional, our results in [14] show that the criterion in [18] cannot be fully recovered as counterexamples exist. This indicates the importance and subtleties of the roles of heterogeneous competition coefficients in the dynamics of the Lotka-Volterra competition-diffusion systems. Our results apply to competition-diffusion-advection systems as well. (See Corollary 5.1 in the last section.

show abstract

Another approach to elliptic eigenvalue problems with respect to indefinite weight functions

Cited by 8 publications

References 6 publications

On eigenvalue problems of 𝑝-Laplacian with Neumann boundary conditions

On eigenvalue problems of 𝑝-Laplacian with Neumann boundary conditions

On the asymptotic distribution of the eigenvalue branches of the Schrödinger operator HW in a spectral gap of H.

Global dynamics of a general Lotka-Volterra competition-diffusion system in heterogeneous environments

Contact Info

Product

Resources

About