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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars:Multiple solutions for semilinear subelliptic Dirichlet problem。
We will discuss the existence of blowup solutions to $u_t=\Delta u+|u|^\frac{4}{n-2}u-|u|^{q-1}u$ with $0ere are three kinds of blowup solutions in this equation. I...
We give a positive lower bound for the principal curvature of the strict convex level sets of harmonic functions in terms of the principal curvature of the domain boundary and the norm of the boundary...
We consider a two-component system of semilinear wave equations in three space dimensions with quadratic nonlinear terms not satisfying the null condition. We prove small data global existence of the ...
We establish new bounds of the Sobolev norms of solutions of semilinear wave equations for data lying in the Hs, s<1, closure of compactly supported data inside a ball of radius R, with R a fixed and ...
In this paper, the controllability of semilinear evolution inclusions with nonlocal conditions in Banach spaces is investigated when the multivalued map has nonconvex values. The approach used here is...
This paper deals with the existence of S-asymptotically ω-periodic solutions to a class of fractional partial differentialequations. A series of analytical results about S-asymptotically ω-periodic so...
Abstract: A monotonicity approach to the study of the asymptotic behavior near corners of solutions to semilinear elliptic equations in domains with a conical boundary point is discussed. The presence...
Abstract: In this work, we aim to prove algebra properties for generalized Sobolev spaces $W^{s,p} \cap L^\infty$ on a Riemannian manifold, where $W^{s,p}$ is of Bessel-type $W^{s,p}:=(1+L)^{-s/m}(L^p...
Abstract: In this paper, the discretization of a nonlinear wave equation whose nonlinear term is a power function is introduced. The difference equation derived by discretizing the nonlinear wave equa...
In this paper, we address the solution of a semilinear heat equation with variable reaction subject to Dirichlet boundary conditions and nonnegative initial datum. Under some assumptions, we show that...
In this paper, we study the boundary value problem of the classical semilinear parabolic equations ut − u = |u|p−1u.
An optimal control problem governed by semilinear elliptic partial differential equations is con-sidered. The equation is in divergence form with the leading term containing controls. By studying the ...
We prove the existence of infinitely many classical periodic solutions for a class of degenerate semilinear wave equations:utt − uxx + |u|s−1u = f(x, t),for all s > 1. In particular we pro...

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