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1.
Semilinear elliptic equations for the fractional Laplacian involving critical exponential growth 下载免费PDF全文
Manassés de Souza Yane Lisley Araújo 《Mathematical Methods in the Applied Sciences》2017,40(5):1757-1772
We establish the existence and multiplicity of weak solutions for a class of nonlocal equations involving the fractional Laplacian operator, nonlinearities with critical exponential growth, and potentials that may change sign. The proofs of our existence results rely on minimization methods and the mountain pass theorem. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
2.
We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system where are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation. 相似文献
3.
On nonlinear perturbations of a periodic fractional Schrödinger equation with critical exponential growth 下载免费PDF全文
In this paper we study the existence of solutions for fractional Schrödinger equations of the form where V is a potential bounded and the nonlinear term has the critical exponential growth. We prove the existence of at least one weak solution by combining the mountain‐pass theorem with the Trudinger–Moser inequality and a version of a result due to Lions for critical growth in . 相似文献
4.
On a class of Hamiltonian elliptic systems involving unbounded or decaying potentials in dimension two 下载免费PDF全文
Francisco S. B. Albuquerque João Marcos do Ó Everaldo S. Medeiros 《Mathematische Nachrichten》2016,289(13):1568-1584
This paper is concerned with the existence of solutions for a class of Hamiltonian elliptic systems with unbounded, singular or decaying radial potentials and nonlinearities having exponential critical growth. The approach relies on an approximation procedure and a version of the Trudinger–Moser inequality. 相似文献
5.
In this article, the following concave and convex nonlinearities elliptic equations involving critical growth is considered,{-△u=g(x)|u|2*-2u+λf(x)|u|q-2u,x∈Ω,u=0,x∈■Ω where Ω■R~N(N≥3) is an open bounded domain with smooth boundary, 1 q 2, λ 0.2*=2 N/(N-2)is the critical Sobolev exponent,f∈L2~*/(2~*-q)(Ω)is nonzero and nonnegative,and g ∈ C(■) is a positive function with k local maximum points. By the Nehari method and variational method,k+1 positive solutions are obtained. Our results complement and optimize the previous work by Lin [MR2870946, Nonlinear Anal. 75(2012) 2660-2671]. 相似文献
6.
Semiclassical ground state solutions for a Schrödinger equation in with critical exponential growth 下载免费PDF全文
Consider a Schrödinger equation where and are two continuous real functions on , ε is a positive parameter, the nonlinearity f is assumed to be of critical exponential growth in the sense of the Trudinger‐Moser inequality. By truncating the potentials and , we are able to establish some new existence and concentration results for critical Schrödinger equation in by variational methods. As a particular case, we observe that the concentration appears at the maximum set of the nonlinear potential which complements the results in 6 , 23 . 相似文献
7.
《Mathematische Nachrichten》2018,291(14-15):2272-2287
The main purpose of this paper is to study the existence of extremal functions for the singular Trudinger–Moser inequalities in the critical case in . More precisely, let and denote then we will prove in this article that there exists such that can be achieved for all , . 相似文献
8.
Elves A. B. Silva Magda S. Xavier 《NoDEA : Nonlinear Differential Equations and Applications》2007,13(5-6):619-642
We study the existence of multiple solutions for a quasilinear elliptic system of gradient type with critical growth and the
possibility of coupling on the subcritical term. The solutions are obtained from a version of the Symmetric Mountain Pass
Theorem. The Concentration-Compactness Principle allows to verify that the Palais-Smale condition is satisfied below a certain
level.
The authors were partially supported by CNPq/Brazil 相似文献
9.
Zhouxin Li 《Journal of Differential Equations》2019,266(11):7264-7290
We prove the existence of positive solutions of the following singular quasilinear Schrödinger equations at critical growth via variational methods, where , , , , . It is interesting that we do not need to add a weight function to control . 相似文献
10.
This paper is concerned with the positive solutions for generalized quasilinear Schrödinger equations in RN with critical growth which have appeared from plasma physics, as well as high-power ultrashort laser in matter. By using a change of variables and variational argument, we obtain the existence of positive solutions for the given problem. 相似文献
11.
Qi Han 《Bulletin des Sciences Mathématiques》2017,141(1):46-71
In this paper, we study mainly the existence of multiple positive solutions for a quasilinear elliptic equation of the following form on , when ,
(0.1)
Here, is a suitable potential function, , is a continuous function of N-superlinear and subcritical exponential growth without having the Ambrosetti–Rabinowitz condition, while is a constant. A suitable Moser–Trudinger inequality and the compact embedding are proved to study problem (0.1). Moreover, the compact embedding is also analyzed to investigate the existence of a positive ground state to the following nonlinear Schrödinger equation(0.2)
with potentials vanishing at infinity in a measure-theoretic sense when . 相似文献
12.
Antonella Marini Thomas H. Otway 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2014
Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge–Bäcklund transformation, underlying symmetries among superficially different forms of the equations. 相似文献
13.
Using a recent result of Ricceri [10] we prove a multiplicity result for a class of quasilinear eigenvalue problems with nonlinear
boundary conditions on an unbounded domain. Our paper completes previous results obtained by Carstea and Rădulescu [4], Chabrowski
[1], [2], Kandilakis and Lyberopoulos [6] and Pflüger [7].
Received: 17 April 2007 相似文献
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15.
This paper addresses the analysis of the weak solution of in a bounded domain Ω subject to the boundary condition on , when the data f belongs to and . We prove existence and uniqueness of solution for this problem in the Nikolskii space . Moreover, we obtain energy estimates regarding the Nikolskii norm of ω in terms of the norm of f. 相似文献
16.
Chen Huang 《Journal of Mathematical Analysis and Applications》2022,505(2):125496
This paper considers the following general form of quasilinear elliptic equation with a small perturbation: where is a bounded domain with smooth boundary and small enough. We assume the main term in the equation to have a mountain pass structure but do not suppose any conditions for the perturbation term . Then we prove the equation possesses a positive solution, a negative solution and a sign-changing solution. Moreover, we are able to obtain the asymptotic behavior of these solutions as . 相似文献
17.
《Mathematische Nachrichten》2017,290(2-3):367-381
In this paper, we study the following Kirchhoff type elliptic problem with critical growth: where , and , and the nonlinear growth term reaches the Sobolev critical exponent since for four spatial dimensions. In a non‐radial symmetric function space, we establish a local compactness splitting lemma of critical version to investigate the existence of positive ground state solutions. 相似文献
18.
Bhatia Sumit Kaur 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(8):2368-2382
Let Ω be a bounded domain in RN,N≥2, with C2 boundary. In this work, we study the existence of multiple positive solutions of the following problem:
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20.
Changlin Xiang 《数学物理学报(B辑英文版)》2017,37(1):58
This note is a continuation of the work[17].We study the following quasilinear elliptic equations(■)where 1 p N,0 ≤μ ((N-p)/p)~p and Q ∈ L~∞(R~N).Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity. 相似文献