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Results tagged with differential-equations
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user 129014
Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.
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Biharmonic equation
Let us consider for $0<\alpha\leq V(x)\leq \beta$ and $0\leq K(x)<\gamma$ the equation
\begin{equation}\label{\star}
\Delta^2u+V(x)u=g(x, u)+K(x)u,
\end{equation}
where $|g(x,s)|\leq \varepsilon|s|^{1 …
- 69
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How can i show that the last equality in the text is true?
Suppose that $v$ is critical point of
$$
f(u)=\frac{1}{2} \int_D|\nabla u|^2-\frac{1}{p+1} \int_D|u|^{p+1}, \quad u \in H_{0, \text{rad}}^1(D),\quad D(r, d)=\left\{z \in R^N: r^2<|z|^2<(r+d)^2\right\} …
- 69