Existence and multiplicity results for a doubly nonlocal equation with critical growth

Existence and multiplicity of positive solutions to Schrödinger–Poisson type systems with critical nonlocal term

The existence, nonexistence and multiplicity of positive radially symmetric solutions to a class of Schrödinger–Poisson type systems with critical nonlocal term are studied with variational methods. The existence of both the ground state solution and mountain pass type solutions are proved. It is shown that the parameter ranges of existence and nonexistence of positive solutions for the critica...

Existence and Blow-up for a Nonlocal Degenerate Parabolic Equation

In this paper, we establish the local existence and uniqueness of the solution for the degenerate parabolic equation with a nonlocal source and homogeneous Dirichlet boundary condition. Moreover, we prove that the solution blows up in finite time and obtain the blow-up set in some special case. Mathematics Subject Classification: 35K20, 35K30, 35K65

Existence and Multiplicity for Perturbations of an Equation Involving Hardy Inequality and Critical Sobolev

For h ≡ 0, k ≡ 1 the problem is studied by S. Terracini in [18]. In [11] the existence of a positive solution is proved in the case h = 0 by using the perturbative method by Ambrosetti-Badiale in [2], even for a more general class of differential operators related to the Caffarelli-Kohn-Nirenberg inequalities that contains our operator. By the perturbative nature of the method, the solutions fo...

An existence results on positive solutions for a reaction-diffusion model with logistics growth and indefinite weight

In this paper, using sub-supersolution argument, we prove an existence result on positive solution for an ecological model under certain conditions. It also describes the dynamics of the fish population with natural predation and constant yield harvesting. The assumptions are that the ecosystem is spatially homogeneous and the herbivore density is a constant which are valid assumptions for mana...

Existence Results for Stochastic Semilinear Differential Inclusions with Nonlocal Conditions