Sobolev norms of radially symmetric oscillatory solutions for superlinear elliptic equations

Radially Symmetric Solutions of a Nonlinear Elliptic Equation

We investigate the existence and asymptotic behavior of positive, radially symmetric singular solutions of w′′ N − 1 /r w′ − |w|p−1w 0, r > 0. We focus on the parameter regime N > 2 and 1 < p < N/ N − 2 where the equation has the closed form, positive singular solution w1 4 − 2 N − 2 p − 1 / p − 1 2 1/ p−1 r−2/ p−1 , r > 0. Our advance is to develop a technique to efficiently classify the behav...

Solutions of Superlinear at Zero Elliptic Equations via Morse Theory

(1) { −∆u = f(u) in Ω, u = 0 on ∂Ω, where Ω ⊂ R is an open bounded domain with smooth boundary. We assume that f ∈ C(R,R) satisfies f(0) = 0, so the constant function u ≡ 0 is a trivial solution of (1). We are interested in the existence of nontrivial solutions when f is superlinear at zero, that is near zero it looks like O(u|u|ν−2) for some ν ∈ (1, 2). More precisely, we assume that f and its...

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

Nodal Solutions of Elliptic Equations with Critical Sobolev Exponents

On the Number of Radially Symmetric Solutions to Dirichlet Problems with Jumping Nonlinearities of Superlinear Order

This paper is concerned with the multiplicity of radially symmetric solutions u(x) to the Dirichlet problem ∆u+ f(u) = h(x) + cφ(x) on the unit ball Ω ⊂ RN with boundary condition u = 0 on ∂Ω. Here φ(x) is a positive function and f(u) is a function that is superlinear (but of subcritical growth) for large positive u, while for large negative u we have that f ′(u) < μ, where μ is the smallest po...