Multiplicity for a strongly singular quasilinear problem via bifurcation theory

نویسندگان

چکیده

A [Formula: see text]-Laplacian elliptic problem in the presence of both strongly singular and text]-superlinear nonlinearities is considered. We employ bifurcation theory, approximation techniques sub-supersolution method to establish existence an unbounded branch positive solutions, which bounded text]-direction bifurcates from infinity at text]. As consequence result, we determine intervals existence, nonexistence particular cases, global multiplicity.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Multiplicity Results for a Singular and Quasilinear Equation

In this paper, we investigate the following quasilinear and singular problem : { −∆pu = λ uδ + u q in Ω u|∂Ω = 0 , u > 0 in Ω (1) where Ω is an open bounded domain with smooth boundary, 1 < p, p− 1 < q and λ, δ > 0. We first prove that there exist weak solutions for λ > 0 small in W 1,p 0 (Ω)∩C(Ω̄) if and only if δ < 2+ 1 p−1 . Investigating the radial symmetric case (Ω = BR(0)), we prove by a s...

متن کامل

Existence and multiplicity of positive solutions for singular quasilinear problems

In this work we combine perturbation arguments and variational methods to study the existence and multiplicity of positive solutions for a class of singular p-Laplacian problems. In the first two theorems we prove the existence of solutions in the sense of distributions. By strengthening the hypotheses, in the third and last result, we establish the existence of two ordered positive weak soluti...

متن کامل

A quasilinear parabolic singular perturbation problem

in a pointwise sense and in a viscosity sense. Here uν denotes the derivative of u with respect to the inward unit spatial normal ν to the free boundary ∂{u > 0}, M = ∫ β(s) ds, α(ν,M) := Φ−1 ν (M) andΦν(α) := −A(αν)+αν ·F(αν), where A(p) is such that F(p) = ∇A(p) with A(0) = 0. Some of the results obtained are new even when the operator under consideration is linear. 2000 Mathematics Subject C...

متن کامل

Multiplicity of Solutions for a Quasilinear Problem with Supercritical Growth

The multiplicity and concentration of positive solutions are established for the equation − ∆pu+ V (z)|u|p−2u = |u|q−2u+ λ|u|s−2u in R , where 1 < p < N , > 0, p < q < p∗ ≤ s, p∗ = Np N−p , λ ≥ 0 and V is a positive continuous function.

متن کامل

Multiplicity of Positive Solutions for a Fourth-Order Quasilinear Singular Differential Equation

This paper is concerned with the multiplicity of positive solutions of boundary value problem for the fourth-order quasilinear singular differential equation (|u|u) = λg(t)f(u), 0 < t < 1, where p > 1, λ > 0. We apply the fixed point index theory and the upper and lower solutions method to investigate the multiplicity of positive solutions. We have found a threshold λ < +∞, such that if 0 < λ ≤...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Bulletin of mathematical sciences

سال: 2022

ISSN: ['1664-3607', '1664-3615']

DOI: https://doi.org/10.1142/s1664360722500138