A Kirchhoff-type problem involving concave-convex nonlinearities

نویسندگان

چکیده

Abstract A Kirchhoff-type problem with concave-convex nonlinearities is studied. By constrained variational methods on a Nehari manifold, we prove that this has sign-changing solution least energy. Moreover, show the energy level of strictly larger than double ground state solution.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود 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

Multiple Positive Solutions for Kirchhoff Type Problems Involving Concave and Convex Nonlinearities in R

In this article, we consider the multiplicity of positive solutions for a class of Kirchhoff type problems with concave and convex nonlinearities. Under appropriate assumptions, we prove that the problem has at least two positive solutions, moreover, one of which is a positive ground state solution. Our approach is mainly based on the Nehari manifold, Ekeland variational principle and the theor...

متن کامل

MULTIPLE SOLUTIONS FOR A CLASS OF p(x)-LAPLACIAN PROBLEMS INVOLVING CONCAVE-CONVEX NONLINEARITIES

Since A. Ambrosetti and P.H. Rabinowitz proposed the mountain pass theorem in 1973 (see [1]), critical point theory has become one of the main tools for finding solutions to elliptic problems of variational type. Especially, elliptic problem (1.2) has been intensively studied for many years. One of the very important hypotheses usually imposed on the nonlinearities is the following Ambrosetti-R...

متن کامل

Multiple results for critical quasilinear elliptic systems involving concave-convex nonlinearities and sign-changing weight functions∗

This paper is devoted to study the multiplicity of nontrivial nonnegative or positive solutions to the following systems    −4pu = λa1(x)|u|q−2u + b(x)Fu(u, v), in Ω, −4pv = λa2(x)|v|q−2v + b(x)Fv(u, v), in Ω, u = v = 0, on ∂Ω, where Ω ⊂ R is a bounded domain with smooth boundary ∂Ω; 1 < q < p < N , p∗ = Np N−p ; 4pw = div(|∇w|p−2∇w) denotes the p-Laplacian operator; λ > 0 is a positive pa...

متن کامل

On the Elliptic Problems Involving Multisingular Inverse Square Potentials and Concave-Convex Nonlinearities

and Applied Analysis 3 conditions on masses and location of singularities for the minimum to be achieved. In 9 , both the case of the whole R and bounded domains are taken into account. To proceed, wemake somemotivations of the present paper. In 6 , the authors studied more general problem than problem 1.5 with μ ∈ 0, μ , s 0, and they proved that there exists Λ > 0 such that problem 1.5 has at...

متن کامل

EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR DEGENERATE p(x)-LAPLACE EQUATIONS INVOLVING CONCAVE-CONVEX TYPE NONLINEARITIES WITH TWO PARAMETERS

We show the existence of two nontrivial nonnegative solutions and infinitely many solutions for degenerate p(x)-Laplace equations involving concaveconvex type nonlinearities with two parameters. By investigating the order of concave and convex terms and using a variational method, we determine the existence according to the range of each parameter. Some Caffarelli-Kohn-Nirenberg type problems w...

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: Advances in Difference Equations

سال: 2021

ISSN: ['1687-1839', '1687-1847']

DOI: https://doi.org/10.1186/s13662-021-03331-x