EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A CLASS OF SUPERLINEAR p-LAPLACIAN EQUATIONS
نویسنده
چکیده
By a variant version of mountain pass theorem, the existence and multiplicity of solutions are obtained for a class of superlinear p-Laplacian equations: −Δ p u = f (x,u). In this paper, we suppose neither f satisfies the superquadratic condition in Ambrosetti-Rabinowitz sense nor f (x,t)/|t| p−1 is nondecreasing with respect to |t|. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution , and reproduction in any medium, provided the original work is properly cited.
منابع مشابه
Multiplicity of solutions for p-Laplacian equation in R with indefinite weight
In this article, we study the existence of infinitely many nontrivial solutions for a class of superlinear p-Laplacian equations −∆pu+ V (x)|u| p−2 u = f(x, u), where the primitive of the nonlinearity f is of subcritical growth near ∞ in u and the weight function V is allowed to be sign-changing. Our results extend the recent results of Zhang and Xu [Q. Y. Zhang, B. Xu, Multiplicity of solution...
متن کاملInfinitely Many Homoclinic Solutions for Second Order Nonlinear Difference Equations with p-Laplacian
We employ Nehari manifold methods and critical point theory to study the existence of nontrivial homoclinic solutions of discrete p-Laplacian equations with a coercive weight function and superlinear nonlinearity. Without assuming the classical Ambrosetti-Rabinowitz condition and without any periodicity assumptions, we prove the existence and multiplicity results of the equations.
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 کاملExistence and Multiplicity of Solutions for p-Laplacian Equations without the AR Condition
The Ambrosetti-Rabinowitz (AR) condition is crucial in variational methods. In this paper we consider a class of p-Laplacian equations without the AR condition. Using Mountain pass lemma and Ekeland variational principle, we obtain the existence and multiplicity of the solutions. These results complement some known results.
متن کاملThe 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 کامل