For any future commenters, here's cleaned up source code. OP, at least check your post. How can anyone understand that code?

var g = new L.GPX('<?php echo APP_BASE;?><?php echo $gpx; ?>', {
    async: true,
    marker_options: {
        startIconUrl: '<?php echo APP_BASE;?>/leaflet-elevator/lib/leaflet-gpx/pin-icon-start.png',
        endIconUrl: '<?php echo APP_BASE;?>/leaflet-elevator/lib/leaflet-gpx/pin-icon-end.png',
        shadowUrl: '<?php echo APP_BASE;?>/leaflet-elevator/lib/leaflet-gpx/pin-shadow.png'
    }
});

var g = new L.GPX({
    {
        URL::asset({
            {
                $trail - > gpx
            }
        })
    }
}, {
    async: true,
    marker_options: {
        startIconUrl: {
            {
                URL::asset('/leaflet-elevator/lib/leaflet-gpx/pin-icon-start.png')
            }
        },
        endIconUrl: {
            {
                URL::asset('/leaflet-elevator/lib/leaflet-gpx/pin-icon-end.png')
            }
        },
        shadowUrl: {
            {
                URL::asset('/leaflet-elevator/lib/leaflet-gpx/pin-shadow.png')
            }
        }
    }
});

Anyway, what errors do you get when you run the code? Could you copy and paste error messages from your browser console?