Existence of solutions for fourth order elliptic equations of Kirchhoff type on RN

In this paper, we study the positive solutions to a class of fourth order elliptic equations of Kirchhoff type on $R^N$ by using variational methods and the truncation method

Periodic solutions for second order singular differential systems with parameters

In this paper we consider the existence of periodic solutions of one-parameter and two-parameter families of second order singular differential equations

Positive Solutions for Singular Complementary Lidstone Boundary Value Problems

By using fixed-point theorems of a cone, we investigate the existence and multiplicity of positive solutions for complementary Lidstone boundary value problems: (−1)(2+1)()=ℎ()(()), in 0<<1, (0)=0, (2+1)(0)=(2+1)(1)=0, 0≤≤−1, where ∈

Two weight inequality for Hankel form on weighted Bergman spaces induced by doubling weights

The boundedness of the small Hankel operator $h_f^\nu(g)=P_\nu(f\bar{g})$, induced by an analytic symbol $f$ and the Bergman projection $P_\nu$ associated to $\nu$, acting from the weighted Bergman space A^p_\om to $A^q_\nu$ is characterized on the full range $0<p,q<\infty$ when $\omega,\nu$ belong to the class $\mathcal{D}$ of radial weights admitting certain two-sided doubling conditions. Certain results obtained are equivalent to the boundedness of bilinear Hankel forms, which are in turn used to establish the weak factorization $A_{\eta}^{q}=A_{\omega}^{p_{1}}\odot A_{\nu}^{p_{2}}$, where $1<q,p_{1},p_{2}<\infty$ such that $q^{-1}=p_{1}^{-1}+p_{2}^{-1}$ and $\widetilde{\eta}^{\frac{1}{q}}\asymp\widetilde{\omega}^{\frac{1}{p_{1}}}\widetilde{\nu}^{\frac{1}{p_{2}}}$. Here $\widetilde{\tau}(r)=\int_r^1\tau(t)\,dt/(1-t)$ for all $0\le r<1$