论文标题
涉及非Ambrosetti-Rabinowitz条件的非局部集成差异操作员的椭圆问题的多重性结果
Multiplicity results for elliptic problems involving nonlocal integrodifferential operators without Ambrosetti-Rabinowitz condition
论文作者
论文摘要
在本文中，我们研究了一般类椭圆方程（\ Mathscr {p}_λ）的弱解决方案的存在和多样性，由非局部分化算子\ Mathscr {l} _ {\ Mathcal a} a} k}的非局部整合算子\ Mathscr {l} k} comention cons驱动，并涉及diricle {a} k}。生长条件。使用山地定理的不同版本，以及带有cerami条件的喷泉定理和双喷泉定理，我们获得了问题的存在薄弱解决方案（\ Mathscr {p}_λ），我们表明，所处理的问题至少具有一个不可接受的解决方案，以适用于任何参数λ> 0的范围λ> 0的范围。此外，λ\至0。对于sublinear，通过使用Kajikiya的新版本的对称山间通过定理[36]，我们通过使用新版本的对称山区的定理来对非线性f（x，x，\ cdot）施加其他假设，我们获得了无限的许多弱解决方案的存在，这些解决方案的存在倾向于在fractional so的情况下，这些弱解决方案倾向于为bole frictions sobolev normation> bolev normation> 0。据我们所知，本文的结果在文献中是新的。
In this paper, we study the existence and multiplicity of weak solutions for a general class of elliptic equations (\mathscr{P}_λ) in a smooth bounded domain, driven by a nonlocal integrodifferential operator \mathscr{L}_{\mathcal{A}K} with Dirichlet boundary conditions involving variable exponents without Ambrosetti and Rabinowitz type growth conditions. Using different versions of the Mountain Pass Theorem, as well as, the Fountain Theorem and Dual Fountain Theorem with Cerami condition, we obtain the existence of weak solutions for the problem (\mathscr{P}_λ) and we show that the problem treated has at least one nontrivial solution for any parameter λ>0 small enough as well as that the solution blows up, in the fractional Sobolev norm, as λ\to 0. Moreover, for the case sublinear, by imposing some additional hypotheses on the nonlinearity f(x,\cdot), by using a new version of the symmetric Mountain Pass Theorem due to Kajikiya [36], we obtain the existence of infinitely many weak solutions which tend to be zero, in the fractional Sobolev norm, for any parameter λ>0. As far as we know, the results of this paper are new in the literature.
