Existence of blow-up solutions for a non-linear equation with gradient term in RN

AbstractIn this paper we study the existence of positive large solutions for the equation Δpu+λ|∇u|p−1=ρ(x)f(u) in RN, where f is a non-negative non-decreasing function and ρ is a non-negative continuous function. We show under some hypotheses detailed below the existence of positive solutions which blow up at infinity

General Quasilinear Problems Involving P(X)-Laplacian with Robin Boundary Condition

This paper deals with the existence and multiplicity of solutions for a class of quasilinear problems involving p(x)-Laplace type equation, namely {−div(a(|∇u|p(x))|∇u|p(x)−2∇u)=λf(x,u)n⋅a(|∇u|p(x))|∇u|p(x)−2∇u+b(x)|u|p(x)−2u=g(x,u)inonΩ,∂Ω. Our technical approach is based on variational methods, especially, the mountain pass theorem and the symmetric mountain pass theorem

Existence of blow-up solutions for a non-linear equation with gradient term in RN

AbstractIn this paper we study the existence of positive large solutions for the equation Δpu+λ|∇u|p−1=ρ(x)f(u) in RN, where f is a non-negative non-decreasing function and ρ is a non-negative continuous function. We show under some hypotheses detailed below the existence of positive solutions which blow up at infinity

Association Between Serum Uric Acid and Development of Type 2 Diabetes

OBJECTIVE To systematically evaluate the association between serum uric acid (SUA) level and subsequent development of type 2 diabetes.RESEARCH DESIGN AND METHODS We searched Medline (31 March from 1966 to 2009) and Embase (31 March from 1980 to 2009) for observational cohort studies examining the association between SUA and the risk of type 2 diabetes by manual literature search. Relative risks (RRs) for each 1 mg/dl increase in SUA were pooled by using a random-effects model. The studies included were stratified into subgroups representing different study characteristics, and meta-regression analyses were performed to investigate the effect of these characteristics on the association between SUA level and type 2 diabetes risk.RESULTS The search yielded 11 cohort studies (42,834 participants) that reported 3,305 incident cases of type 2 diabetes during follow-up periods ranging from 2.0 to 13.5 years. The pooled RR of a 1 mg/dl increase in SUA was 1.17 (95% CI 1.09–1.25). Study results were consistently significant (i.e., >1) across characteristics of participants and study design. Publication bias was both visually and statistically suggested (P = 0.03 for Egger\u27s test, 0.06). Adjustment for publication bias attenuated the pooled RR per mg/dl increase in SUA (RR 1.11 [95% CI 1.03–1.20]), but the association remained statistically significant (P = 0.009).CONCLUSIONS The current meta-analysis suggests that SUA level is positively associated with the development of type 2 diabetes regardless of various study characteristics. Further research should attempt to determine whether it is effective to utilize SUA level as a predictor of type 2 diabetes for its primary prevention

On a nonresonance condition between the first and the second eigenvalues for the p-Laplacian

We are concerned with the existence of solution for the Dirichlet problem −Δpu=f(x,u)+h(x) in Ω, u=0 on ∂Ω, when f(x,u) lies in some sense between the first and the second eigenvalues of the p-Laplacian Δp. Extensions to more general operators which are (p−1)-homogeneous at infinity are also considered

Existence of weak solutions for a quasilinear equation in RN

AbstractThis paper studies the p-Laplacian equation −Δpu+λVλ(x)|u|p−2u=f(x,u)inRN, where 1<p<N,λ≥1 and Vλ(x) is a nonnegative continuous function. Under some conditions on f(x,u) and Vλ(x), we prove the existence of nontrivial solutions for λ sufficiently large