论文标题
在涉及特征值问题的非本地非线性非线性椭圆方程
On non-local nonlinear elliptic equations involving an eigenvalue problem
论文作者
论文摘要
本文研究了一类非本地椭圆边界值问题的解决方案的存在和多样性。使用变分方法，我们检查了由于非本地效应而导致的解决方案行为的变化。在相同的规定条件下，在没有非本地项的情况下，在没有椭圆边界值问题的结果与椭圆边界值问题的结果进行了比较，以突出非本地性能对解决方案行为的影响。我们在这里的结果表明，在存在非局部效应的情况下，溶液结构的复杂性显着增加，可能性从无允许的正溶液到三种阳性溶液的可能性，并且与没有非局部术语所获得的溶液相反，解决方案概况也取决于源功能的超线性功能。
The existence and multiplicity of solutions for a class of non-local elliptic boundary value problems with superlinear source functions are investigated in this paper. Using variational methods, we examine the changes arise in the solution behaviours as a result of the non-local effect. Comparisons are made of the results here with those of the elliptic boundary value problem in the absence of the non-local term under the same prescribed conditions to highlight this effect of non-locality on the solution behaviours. Our results here demonstrate that the complexity of the solution structures is significantly increased in the presence of the non-local effect with the possibility ranging from no permissible positive solution to three positive solutions and, contrary to those obtained in the absence of the non-local term, the solution profiles also vary depending on the superlinearity of the source functions.
