共查询到20条相似文献,搜索用时 31 毫秒
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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
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The paper investigates longtime dynamics of the Kirchhoff wave equation with strong damping and critical nonlinearities: , with . The well-posedness and the existence of global and exponential attractors are established, and the stability of the attractors on the perturbation parameter ? is proved for the IBVP of the equation provided that both nonlinearities and are of critical growth. 相似文献
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We prove the existence and multiplicity of positive radial solutions to the nonlinear system for a certain range of , where , , , , are continuous with possible singularity ±∞ at 0 and satisfy a combined superlinear condition at ∞. 相似文献
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《Discrete Mathematics》2022,345(10):113004
Let G be a graph. We say that G is perfectly divisible if for each induced subgraph H of G, can be partitioned into A and B such that is perfect and . We use and to denote a path and a cycle on t vertices, respectively. For two disjoint graphs and , we use to denote the graph with vertex set and edge set , and use to denote the graph with vertex set and edge set . In this paper, we prove that (i) -free graphs are perfectly divisible, (ii) if G is -free with , (iii) if G is -free, and (iv) if G is -free. 相似文献