We construct a sequence of compact, oriented, embedded, two-dimensional surfaces of genus one into Euclidean 3-space with prescribed, almost constant, mean curvature of the form H(X)=1+A|X| −γ for |X| large, when...
We study an elliptic equation related to the Moser–Trudinger inequality on a compact Riemann surface (S,g), Δ gu+λ(ue u 2 −[Formula presented]∫Sue u 2 dv...
We consider the problem vt=Δv+|v|p−1vin Ω×(0,T),v=0on ∂Ω×(0,T),v>0in Ω×(0,T). In a domain Ω⊂Rd, d≥7 enjoying special symmetries, we find the first example of a solution with type II blow-up...
Through desingularization of Clifford torus, we prove the existence of a sequence of nondegenerate (in the sense of Duyckaerts–Kenig–Merle ([8])) nodal nonradial solutions to the critical Yamabe problem −Δu=[Formula...
We consider the wave equation ε2(-∂t2+Δ)u+f(u)=0 for 0 < ε≪ 1 , where f is the derivative of a balanced, double-well potential, the model case being f(u) = u- u3. For equations of this form, we construct...
We consider the problem vt=Δv+|v|p−1vin Ω×(0,T),v=0on ∂Ω×(0,T),v>0in Ω×(0,T). In a domain Ω⊂Rd, d≥7 enjoying special symmetries, we find the first example of a solution with type II blow-up...
We verify the existence of radial positive solutions for the semilinear equation (Formula presented.) where N ≥ 3, p is close to p* ≔ (N+ 2)/(N − 2), and V is a radial smooth potential. If q is super-critical, namely q >...
We study an elliptic equation related to the Moser–Trudinger inequality on a compact Riemann surface (S,g), Δ gu+λ(ue u 2 −[Formula presented]∫Sue u 2 dv...
Through desingularization of Clifford torus, we prove the existence of a sequence of nondegenerate (in the sense of Duyckaerts–Kenig–Merle ([8])) nodal nonradial solutions to the critical Yamabe problem −Δu=[Formula...
Let Ω be a smooth bounded domain in ℝn, n ≥ 5. We consider the classical semilinear heat equation at the critical Sobolev exponent (Equation Presented) Let G(x, y) be the Dirichlet Green function of - A in Q and H(x, y) its...
We consider the wave equation ε2(-∂t2+Δ)u+f(u)=0 for 0 < ε≪ 1 , where f is the derivative of a balanced, double-well potential, the model case being f(u) = u- u3. For equations of this form, we construct...
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