Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...

A new class of nonlinear set-valued variationalinclusions involving $(A,eta)$-monotone mappings in a Banachspace setting is introduced, and then based on the generalizedresolvent operator technique associated with$(A,eta)$-monotonicity, the existence and approximationsolvability of solutions using an iterative algorithm and fixedpint theory is investigated.

We establish the existence and uniqueness of strong solutions to stochastic porous media equations driven by Lévy noise on a $$\sigma $$ -finite measure space $$(E,{\mathcal {B}}(E),\mu )$$ , with Laplacian replaced negative definite self-adjoint operator. The coefficient $$\Psi is only assumed satisfy increasing Lipschitz nonlinearity assumption, without restriction $$r\Psi (r)\rightarrow \inf...

In this note we introduce strongly Lipschitz p-integral operators, strongly Lipschitz p-nuclear operators and Lipschitz p-nuclear operators. It is shown that for a linear operator, the Lipschitz p-nuclear norm is the same as its usual p-nuclear norm under certain conditions. We also prove that the Lipschitz 2-dominated operators and the strongly Lipschitz 2-integral operators are the same with ...

‎In this work we prove Malliavin differentiability for the solution to an SDE with locally Lipschitz and semi-monotone drift‎. ‎To prove this formula‎, ‎we construct a sequence of SDEs with globally Lipschitz drifts and show that the $p$-moments of their Malliavin derivatives are uniformly bounded‎.

We consider the nonlinear Poisson equation $$-\Delta u = f(u)$$ in domains $$\Omega \subset {\mathbb {R}}^n$$ with Dirichlet boundary conditions on $$\partial \Omega $$ . show (for monotonically increasing concave f small Lipschitz constant) that if $$D^2 u$$ is negative semi-definite boundary, then concave. A conjecture of Saint Venant from 1856 (proven by Polya 1948) among all fixed measure, ...