We study a degenerate elliptic system with variable exponents. Using the variational approach and some recent theory on weighted Lebesgue and Sobolev spaces with variable exponents, we prove the existence of at least ...We study a degenerate elliptic system with variable exponents. Using the variational approach and some recent theory on weighted Lebesgue and Sobolev spaces with variable exponents, we prove the existence of at least two distinct nontrivial weak solutions of the system. Several consequences of the main theorem are derived;in particular, the existence of at lease two distinct nontrivial non-negative solutions is established for a scalar degenerate problem. One example is provided to show the applicability of our results.展开更多
In this paper, we consider the following high-order p-Laplacian generalized neutral differential equation with variable parameter(φp(x(t)-c(t)x(t-σ))(n))(m)+ g(t, x(t), x(t-τ(t)), x′(t), ···, x(m)(t...In this paper, we consider the following high-order p-Laplacian generalized neutral differential equation with variable parameter(φp(x(t)-c(t)x(t-σ))(n))(m)+ g(t, x(t), x(t-τ(t)), x′(t), ···, x(m)(t)) = e(t).By the coincidence degree theory and some analysis skills, sufficient conditions for the existence of periodic solutions are established.展开更多
基金supported in part by a University of Tennessee at Chattanooga SimCenter-Center of Excellence in Applied Computational Science and Engineering (CEACSE) grant
文摘We study a degenerate elliptic system with variable exponents. Using the variational approach and some recent theory on weighted Lebesgue and Sobolev spaces with variable exponents, we prove the existence of at least two distinct nontrivial weak solutions of the system. Several consequences of the main theorem are derived;in particular, the existence of at lease two distinct nontrivial non-negative solutions is established for a scalar degenerate problem. One example is provided to show the applicability of our results.
基金supported by National Natural Science Foundation of China(71601072)
文摘In this paper, we consider the following high-order p-Laplacian generalized neutral differential equation with variable parameter(φp(x(t)-c(t)x(t-σ))(n))(m)+ g(t, x(t), x(t-τ(t)), x′(t), ···, x(m)(t)) = e(t).By the coincidence degree theory and some analysis skills, sufficient conditions for the existence of periodic solutions are established.
