Multiplicity of solutions for a class of quasilinear elliptic equations with concave and convex terms in R ∗
نویسنده
چکیده
In this paper the Fountain theorem is employed to establish infinitely many solutions for the class of quasilinear Schrödinger equations −Lpu + V (x)|u|p−2u = λ|u|q−2u + μ|u|r−2u in R, where Lpu = (|u′|p−2u′)′ + (|(u2)′|p−2(u2)′)′u, λ, μ are real parameters, 1 < p <∞, 1 < q < p, r > 2p and the potential V (x) is nonnegative and satisfies a suitable integrability condition. AMS Subject Classification: 35J20, 35J60, 35Q55.
منابع مشابه
The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent
In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.
متن کاملExistence and multiplicity of nontrivial solutions for $p$-Laplacian system with nonlinearities of concave-convex type and sign-changing weight functions
This paper is concerned with the existence of multiple positive solutions for a quasilinear elliptic system involving concave-convex nonlinearities and sign-changing weight functions. With the help of the Nehari manifold and Palais-Smale condition, we prove that the system has at least two nontrivial positive solutions, when the pair of parameters $(lambda,mu)$ belongs to a c...
متن کاملQuasilinear Schrödinger equations involving critical exponents in $mathbb{textbf{R}}^2$
We study the existence of soliton solutions for a class of quasilinear elliptic equation in $mathbb{textbf{R}}^2$ with critical exponential growth. This model has been proposed in the self-channeling of a high-power ultra short laser in matter.
متن کاملExistence Results for a Dirichlet Quasilinear Elliptic Problem
In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.
متن کاملMultiple Solutions for a Class of Concave-Convex Quasilinear Elliptic Systems with Nonlinear Boundary Condition
In this paper, a quasilinear elliptic system is investigated, which involves concave-convex nonlinearities and nonlinear boundary condition. By Nehari manifold, fibering method and analytic techniques, the existence of multiple nontrivial nonnegative solutions to this equation is verified.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008