Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 Opuscula Mathematica

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: semipositone problems

Sortuj według:

Ogranicz wyniki do:

Study of fractional semipositone problems on RN

Biswas Nirjan

Opuscula Mathematica

2024

Vol. 44, no. 4

445--470

Let s ∈ (0, 1) and N > 2s. In this paper, we consider the following class of nonlocal semipositone problems: (−Δ)su = g(x)ƒa(u) in RN, u > 0 in RN, where the weight g ∈ L1(RN) ∩ L∞(RN) is positive, a > 0 is a parameter, and ƒa ∈ C(R) is strictly negative on (−∞, 0]. For ƒa having subcritical growth and weaker Ambrosetti–Rabinowitz type nonlinearity, we prove that the above problem admits a mountain pass solution ua, provided a is near zero. To obtain the positivity of ua, we establish a Brezis–Kato type uniform estimate of (ua) in Lr(RN) for every r ∈ [formula].

Positive stationary solutions of convection-diffusion equations for superlinear sources

Orpel Aleksandra

Opuscula Mathematica

2022

Vol. 42, no. 5

727--749

We investigate the existence and multiplicity of positive stationary solutions for a certain class of convection-diffusion equations in exterior domains. This problem leads to the following elliptic equation Δu(x) + f(x, u(x)) + g(x)x · ∇u(x) = 0, for x ∈ ΩR = {x ∈ Rn, ∥x∥ > R}, n > 2. The goal of this paper is to show that our problem possesses an uncountable number of nondecreasing sequences of minimal solutions with finite energy in a neighborhood of infinity. We also prove that each of these sequences generates another solution of the problem. The case when f(x, ·) may be negative at the origin, so-called semipositone problem, is also considered. Our results are based on a certain iteration schema in which we apply the sub and supersolution method developed by Noussair and Swanson. The approach allows us to consider superlinear problems with convection terms containing functional coefficient g without radial symmetry.