Research Interests:
Research Interests:
Research Interests:
In this paper, we investigate the regularity and symmetry properties of weak solutions to semilinear elliptic equations which are stable or more generally of finite Morse index or even more generally locally stable.
Research Interests:
The paper proves Liouville-type results for stable solutions of semilinear elliptic PDEs with convex nonlinearity, posed on the entire Euclidean space. Extensions to solutions which are stable outside a compact set are also presented.
Several Liouville-type theorems are presented for stable solutions of the equation −1u = f (u) in RN , where f > 0 is a general convex, nondecreasing function. Extensions to solutions which are merely stable outside a compact set are... more
Several Liouville-type theorems are presented for stable solutions of the equation −1u = f (u) in RN , where f > 0 is a general convex, nondecreasing function. Extensions to solutions which are merely stable outside a compact set are discussed.
Research Interests: Mathematics and Delta
Research Interests:
Several Liouville-type theorems are presented for stable solutions of the equation u = f(u) in RN , where f > 0 is a general convex, non- decreasing functions. Extensions to solutions which are merely stable outside a compact set are... more
Several Liouville-type theorems are presented for stable solutions of the equation u = f(u) in RN , where f > 0 is a general convex, non- decreasing functions. Extensions to solutions which are merely stable outside a compact set are discussed.