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We analyse the structure of the set of solutions to the following class ofboundary value problems  \begin{equation}\tag{$P_\lambda$}  -\text{div}(A(x)Du)=c_\lambda(x)u+( M(x)Du,Du)+h(x), \quad u \inH_0^1(\Omega)\cap L^\infty(\Omega)  \end{equation} where $\Omega\subset\mathbb{R}^n$, $n\geq 3$ is a boundeddomain with boundary $\partial\Omega$ of class $C^{1,D}$. We assume that $c,h\in L^p(\Omega)$ for some $p>n$, where $c^{\pm} \geq 0$ are such that$c_\lambda(x):=\lambda c^+(x)-c^-(x)$ for a parameter $\lambda\in\mathbb{R}$,$A(x)$ is a uniformly positive bounded measurable matrix and $M(x)$ is apositive bounded matrix.}  Under suitable assumptions, we describe the continuum of solutions to problem$(P_\lambda)$ and also its bifurcation points proving existence and uniquenessresults in the coercivecase $(\lambda \leq 0)$ and multiplicity results in thenon-coercive case $(\lambda > 0)$.

Multiplicity Results for a Class of Quasilinear Elliptic Problems with Quadratic Growth on the Gradient