共查询到9条相似文献,搜索用时 0 毫秒
1.
We give verifiable conditions ensuring that second order quasilinear elliptic equations on
have infinitely many solutions in the Sobolev space
for generic right-hand sides. This amounts to translating in concrete terms the more elusive hypotheses of an abstract theorem. Salient points include the proof that a key denseness property is equivalent to the existence of nontrivial solutions to an auxiliary problem, and an estimate of the size of the set of critical points of nonlinear Schrödinger operators. Conditions for the real-analyticity of Nemytskii operators are also discussed. 相似文献
2.
We consider the semilinear elliptic problem in Ω, u=0 on ∂Ω, where 0∈Ω is a smooth bounded domain in RN, N?4, , is the critical Sobolev exponent, f(x,⋅) has subcritical growth at infinity, K(x)>0 is continuous. We prove the existence of sign-changing solutions under different assumptions when Ω is a usual domain and a symmetric domain, respectively. 相似文献
3.
4.
Multiple sign-changing solutions for a class of semilinear elliptic equations in $\mathbb{R}^{N}$
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In this paper, we study the following semilinear elliptic equations $$-\triangle u+V(x)u=f(x,u), \ \ x\in \mathbb{R}^{N},$$ where $V\in C(\mathbb{R}^{N}, \mathbb{R})$ and $f\in C(\mathbb{R}^{N}\times\mathbb{R}, \mathbb{R})$. Under some suitable conditions, we prove that the equation has three solutions of mountain pass type: one positive, one negative, and sign-changing. Furthermore, if $f$ is odd with respect to its second variable, this problem has infinitely many sign-changing solutions. 相似文献
5.
Andrew Raich 《Mathematische Zeitschrift》2007,256(1):193-220
Let be a subharmonic, nonharmonic polynomial and a parameter. Define , a closed, densely defined operator on . If and , we solve the heat equations , u(0,z) = f(z) and , . We write the solutions via heat semigroups and show that the solutions can be written as integrals against distributional
kernels. We prove that the kernels are C
∞ off of the diagonal {(s, z, w) : s = 0 and z = w} and find pointwise bounds for the kernels and their derivatives.
相似文献
6.
We study the existence of positive solutions of a linear elliptic
equation with critical Sobolev exponent in a nonlinear Neumann boundary
condition. We prove a result which is similar to a classical result of Brezis
and Nirenberg who considered a corresponding problem with nonlinearity in
the equation. Our proof of the fact that the dimension three is critical uses
a new Pohoaev-type identity.AMS Subject Classification: Primary: 35J65; Secondary: 35B33. 相似文献
7.
We derive several sufficient conditions for the uniform approximability of functions by polynomial solutions of homogeneous elliptic equations of second order with constant coefficients on Carathéodory compact sets in
. 相似文献
8.