Sign-changing solutions and multiplicity results for elliptic problems via lower and upper solutions

Multiplicity of positive solutions for critical singular elliptic systems with sign - changing weight function ∗

In this paper, the existence and multiplicity of positive solutions for a critical singular elliptic system with concave and convex nonlinearity and sign-changing weight function, are established. With the help of the Nehari manifold, we prove that the system has at least two positive solutions via variational methods.

Multiplicity of positive solutions for fractional elliptic systems involving sign-changing weight

In this paper, we study the multiplicity results of positive solutions for a fractional elliptic system involving both concave-convex and critical growth terms. With the help of Morse theory and the Ljusternik-Schnirelmann category, we investigate how the coefficient h(x) of the critical nonlinearity affects the number of positive solutions of that problem and we get some results as regards the...

Multiplicity of Positive Solutions of laplacian systems with sign-changing weight functions

In this paper, we study the multiplicity of positive solutions for the Laplacian systems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic system has at least two positive solutions.

Multiple Solutions and a Sign-Changing Solution for Semi-Linear Elliptic Problems with Resonance

Multiplicity of solutions for quasilinear elliptic boundary-value problems

This paper is concerned with the existence of multiple solutions to the boundary-value problem −(φp(u )) = λφq(u) + f(u) in (0, 1) , u(0) = u(1) = 0 , where p, q > 1, φx(y) = |y| y, λ is a real parameter, and f is a function which may be sublinear, superlinear, or asymmetric. We use the time map method for showing the existence of solutions.